Müller played as a youth for TSV Pähl, and at the age of 10 he made the 50-kilometre (31 mi) journey to join local Bundesliga side Bayern Munich in 2000. He progressed through the youth system and was part of the team that finished runner-up in the Under 19 Bundesliga in 2007.

Müller represented Germany at various youth levels, starting with the under-16s in 2004. In August 2009, he was called up to the under-21 team for his debut in a 3–1 friendly defeat against Turkey. He earned six caps for the under-21s and scored one goal, the eighth in an 11–0 thrashing of San Marino.

He made his debut for the reserve team in March 2008 when he replaced Stephan Fürstner in a Regionalliga match against SpVgg Unterhaching, in which he scored. He made two more Regionalliga appearances in the 2007–08 season, while continuing to play for the under-19 team. The following season, Bayern’s second string qualified for the newly formed 3. Liga, and Müller established himself as a key player – he played in 32 out of 38 matches and scored 15 times to make him the league’s fifth top scorer.

Müller became involved in the first-team under then manager Jürgen Klinsmann; he appeared in pre-season friendlies, and made his full debut on 15 August 2008, when he came on as a substitute for Miroslav Klose for the last ten minutes of a Bundesliga match against Hamburger SV. Despite Müller feeling that his performance did not go well, he made three more Bundesliga appearances that season and made his Champions League debut on 10 March 2009 when he was substituted on in the 72nd minute for Bastian Schweinsteiger in a 7–1 win over Sporting CP. He scored Bayern’s last goal as they won the tie 12–1 on aggregate.

In February 2009, Müller signed his first contract for the senior team, a two-year deal effective from the 2009–10 season, along with reserve teammate Holger Badstuber.

Müller was prepared to be loaned or even transferred away to find first-team football, but when Louis van Gaal was appointed manager, both Müller and Badstuber became fixtures in the Bayern first team from the start of the season. In the first few matches, Müller was a regular substitute, and on 12 September 2009, he was brought on against Borussia Dortmund and scored two goals in a 5–1 victory. Three days later, he scored another brace in a 3–0 Champions League victory over Maccabi Haifa. He rounded off September by being named the Bundesliga Player of the Month and earned praise from his namesake, legendary former Bayern and Germany striker Gerd Müller. After the Haifa match, Müller was in the starting XI for almost every match, only missing one match, a Champions League match against Bordeaux, for which he was suspended, because he was sent off in an earlier match against the same team.

Müller was born in Weilheim in Oberbayern, Bavaria. He grew up in the nearby village of Pähl, which became the centre of media attention during his World Cup exploits. His parents are Klaudia and Gerhard, and he has a brother, Simon, who is two and a half years younger. He married his long-time girlfriend Lisa Trede, a semi-professional equestrian who works on a farm, in December 2009 after being engaged for two years. In June 2011, he became an ambassador for YoungWings, a charity that helps children who have suffered bereavement or trauma. He is Roman Catholic.

In February 2010, Müller signed a new contract with Bayern Munich through 2013. During the second half of the season, Müller continued to be a regular first-team starter, usually playing in a central striking role due to the availability of other wide players Franck Ribéry and Arjen Robben. In April 2010, he scored the second goal in a 2–1 win against title rivals Schalke 04, and in the penultimate league match of the season, he scored the first hat-trick of his career, in a 3–1 win over VfL Bochum which effectively secured the German title for Bayern. The title was confirmed a week later with a 3–1 win at Hertha BSC, a match which Müller started.

For the season, he played in all 34 Bundesliga matches, starting 29, and recorded 13 goals and 11 assists. Bayern and Müller were back in Berlin the following week, to face Werder Bremen in the final of the DFB-Pokal. Müller started the match and Bayern won 4–0 to complete the domestic double. Müller scored four goals and made two assists during the competition, which made him its leading scorer for the season. Bayern’s season ended in pursuit of a first treble, in the 2010 Champions League Final against Inter Milan at Santiago Bernabéu Stadium in Madrid. It was not to be, however, as they lost 2–0, with both goals coming from Diego Milito. Müller was in the starting line-up and had a key chance just after half-time, with Bayern 1–0 down, but his shot was saved by Júlio César. Müller felt particularly disappointed by this defeat, but he ended his first season as a first-team player with 52 matches played and 19 goals in all competitions.

He was back in the senior squad for its next get-together, a training session in Sindelfingen in January 2010, and was named in the squad for the following match, a friendly against Argentina in March. He made his debut in this game in the starting XI at the Allianz Arena, his home stadium with Bayern. He was substituted in the 66th minute for fellow debutant Toni Kroos as Germany lost 1–0.

In October 2010, he was named on the shortlist for the FIFA Ballon d’Or award along with four of his Germany teammates. Reflecting on his World Cup success, Müller said “I basically got lucky, I hit form at just the right time”.

In Bayern’s first DFB-Pokal game Müller was awarded the man of the match after earning two penalties which were converted by Mario Gómez and Bastian Schweinsteiger, Müller then added a third in the closing stages to secure a 3–0 victory over Eintracht Braunschweig. It took Müller five matches for him to get his first league goal; he scored it against Schalke 04 in Bayern’s 2–0 win. Müller then scored in Bayern’s next home game in the early stages of the match, which they went on to win, 3–0. On 26 November 2011, Müller netted the opener on the half-hour in Bayern’s 6–0 thrashing of FC Ingolstadt, giving him his second DFB-Pokal goal. Müller was on the short-list of this year’s FIFA Ballon d’Or award. On 10 and 15 January, in Bayern’s warm up friendlies, Müller scored three goals in two games, a brace against the India national team (which Bayern then went on to win 4–0) and one goal in Bayern’s other 4–0 victory over Rot-Weiß Erfurt. Müller provided two assists in Bayern’s win over VfB Stuttgart in the DFB-Pokal.

Müller started all ten of Germany’s qualifiers for Euro 2012, as the team qualified for the finals with a 100% record. Müller provided assists for seven goals, three of which came in a 6–2 win over Austria in September 2011 which secured Germany’s qualification for the finals with two games to spare. He scored three times in the campaign, two goals coming in a 4–0 win over Kazakhstan in March 2011, the third in a 3–1 win over Turkey in October of the same year.

On 11 February, Bayern played 1. FC Kaiserslautern and Müller ended a goal drought lasting since 24 September 2011 with a header in their 2–0 victory. On 31 March 2012, Müller played his 100th Bundesliga game against 1. FC Nürnberg. On 19 May 2012, Müller scored the opening goal in the Champions League final against Chelsea with a powerful header. He was substituted shortly afterwards. Bayern Munich, however, lost the final on penalties. Müller stated how dissatisfied he was about the amount of time he had spent on the bench recently. Müller said that although he was dissatisfied he wanted to stay at Bayern. During the season, Müller scored seven goals in 34 league matches, two goals in five German Cup matches, and two goals in 14 Champions League matches.

Müller’s first Bundesliga goal of the season came over 2. Bundesliga champions SpVgg Greuther Fürth in Bayern’s 3–0 victory on 27 August 2012. On 2 September, he netted a brace as Bayern thrashed southern rivals VfB Stuttgart, 6–1, in front of 71,000 at the newly expanded Allianz Arena. Müller helped Bayern achieve a record-breaking start to the league season, when he netted a brace over newly promoted Fortuna Düsseldorf on 20 October in their 5–0 victory, recording Bayern’s eighth successive win. Three days later, he scored his first Champions League goal of the season, netting from the penalty spot, as Bayern defeated Lille 1–0 at the French side’s newly built Grand Stade Lille Métropole.

On 13 December, after his good run of form in the first half of the Bundesliga season, Müller pledged his allegiance claiming he was at home in Munich and that, “There is no club to step up from when you leave FC Bayern… there almost is no better club.” Six days later, he signed a two-year contract extension, keeping him at the Allianz Arena until 2017. At the winter break in the Bundesliga, he had nine goals and seven assists in 16 league appearances and a further three goals in the Champions League; this gave him a total of 13 goals halfway through the season, including his strike against Borussia Dortmund in Bayern’s win in the 2012 DFL-Supercup. Müller scored his first goal in Bayern’s second game back from the break in a 2–0 away win over VfB Stuttgart. Müller tapped in his fifth goal of the Champions League campaign on 2 April, completing a 2–0 first leg defeat of Juventus in the quarter-finals, ending the Italian club’s 18-match unbeaten record in Europe.

On 23 April 2013, Müller scored two goals and gave one assist in 4–0 win against Barcelona in the Champions League semi-final in the Allianz Arena. On the return fixture, Müller scored a header as Bayern won 3–0 and gave Barcelona their biggest defeat ever in the Champions League, with a 7–0 aggregate score. Müller then went on to play an important role in Bayern’s 2–1 victory over Borussia Dortmund in the final. On 1 June, Müller scored a penalty in the final of the 2012–13 DFB-Pokal. Bayern won the cup 3–2 to complete an historic treble. Müller scored 23 goals overall in the season (including all competitions), netting 13 in the Bundesliga, one in the Pokal, and an impressive eight in the Champions League, he also added one in the 2012 DFL-Supercup which Bayern won 2–1.

Müller scored his first World Cup qualifying goals on 22 March 2013, scoring Germany’s opener and final goal in a 3–0 away win over Kazakhstan. He also scored in the 3–0 victories over Austria and the Faroe Islands to give him four goals in Germany’s successful qualification campaign.

On 17 May 2014, Müller scored Bayern’s second goal in a 2–0 extra-time defeat of Borussia Dortmund in the 2014 DFB-Pokal Final, giving die Roten the tenth league and cup double in their history. Müller finished as the tournament’s top scorer with eight goals in five appearances. He finished the season by scoring 13 goals in 31 league matches, eight goals in five DFB-Pokal matches, and five goals in 12 Champions League matches.

After the 2013–14 season, Müller signed a new contract keeping him at Bayern until 2019 and rejected a contract offer from Manchester United. Müller played in the DFL-Supercup, which was Bayern’s first match in the 2014–15 season. Bayern lost the match 2–0. His first goal of the season was against Preußen Münster in the DFB-Pokal on 17 August 2014. Then in the opening match of the Bundesliga, on 22 August 2014, Müller scored the opening goal of Bayern’s Bundesliga season against VfL Wolfsburg. Bayern went on to win the match 2–1.

On 16 June 2014, in Germany’s opening match of the 2014 World Cup, Müller scored the first hat-trick of the tournament and was named man of the match in a 4–0 win against Portugal. In addition, he was also the target of Pepe’s headbutt in the 37th minute, which resulted in the Portuguese defender being sent off. He denied that he had “overplayed” the situation leading to the red card. On 26 June, Müller scored the only goal of the final group match against the United States to help the Germans win Group G and dispelled fear of collusion between German coach Joachim Löw and American coach Jürgen Klinsmann to play to a draw as had occurred in 1982.

On 11 March 2015, Müller scored two goals against Shakhtar Donetsk in a 7–0 win to draw level with former teammate Mario Gómez as the top-scoring German player in UEFA Champions League history. He subsequently became the leader when he scored in a 6–1 win against Porto on 21 April 2015. He finished the season with 13 goals in 32 league matches, a goal in five DFB-Pokal matches, and seven goals in ten Champions League matches.

On 9 December 2015, Müller came on as a 46th-minute substitute for Franck Ribéry in a 2–0 win against Dinamo Zagreb. He failed to convert his penalty shot in the match and finished the group stage with five goals from six appearances. On 18 December 2015, Müller signed a new contract with Bayern, keeping him at the club until 2021. On 19 December 2015, Bayern defeated Hannover 96 1–0 with a goal from the penalty mark from Müller. Bayern went on winter break after the match. Müller finished the first half of the league with 14 goals from 17 appearances. This includes scoring five goals from the penalty mark in six opportunities. He had scored 21 goals in 25 appearances in all competitions up until the winter break.

On 12 March 2016, Müller scored a brace in a 5–0 victory over Werder Bremen. Four days later, with Bayern trailing Juventus 1–2 in the second leg of the Champions League round of 16, he scored a 91st-minute equaliser before Bayern won in extra time 4–2 (6–4 aggregate). On 19 April 2016, Müller scored both goals in Bayern’s 2–0 defeat of Werder Bremen in the DFB-Pokal semi-final. His first goal of the match was his 150th for the club in all competitions. On 3 May 2016, Müller had a penalty kick saved by Jan Oblak in the Champions League semi-final second leg at home to Atlético Madrid. The match ended in a 2–1 win for Bayern but the team was knocked out on the away goals rule. He finished the season by scoring 20 goals in 31 league matches, 4 goals in 5 German Cup matches, and 8 goals in 12 Champions League matches. He didn’t score in the German Super Cup. With 32 goals in all Competitions, this was Müller’s most prolific season to date.

Müller started the season by winning and scoring in the 2016 German Super Cup against Borussia Dortmund on 14 August 2016. In the league, Müller did not score for 999 minutes until he scored during a home game against VfL Wolfsburg in the 76th minute. He finished the 2016–17 season by scoring five goals in 29 Bundesliga appearances, no goals in three German Cup appearances, and three goals in nine Champions League appearances. Müller did have a career best 12 assists in the Bundesliga.

Müller started the 2017–18 season by playing in the 2017 German Super Cup. He played in the opening 67 minutes before being replaced by Kingsley Coman. His first goal of the season was against Mainz on matchday four of the Bundesliga. On 21 January 2018, he scored two goals against Werder Bremen in the Bundesliga, with his second goal in the match being his 100th in the competition. On 20 February 2018, Müller scored two goals against Beşiktaş in Champions League.

Müller started the 2018–19 season by starting in the German Super Cup. Müller scored in the first two matchdays in the Bundesliga season. He scored in the second round of the German Cup against SV Rödinghausen. He scored two goals against Fortuna Düsseldorf in the Bundesliga on 24 November 2018. On 12 December 2018, Müller played his 105th Champions League match in a match against Ajax and therefore leveling former club legend Philipp Lahm as the record appearance holder in the Champions League at Bayern. In that same match Müller was sent off for the first time in his career for a straight red card. This resulted in a two-match suspension. On 15 December 2018, Müller made his 300th Bundesliga appearance for Bayern against Hannover 96.

On 18 May 2019, Müller won his seventh consecutive Bundesliga title as Bayern finished two points above Dortmund with 78 points. It was Müller’s eighth Bundesliga title. A week later, Müller won his fifth DFB-Pokal as Bayern defeated RB Leipzig 3–0 in the 2019 DFB-Pokal Final. He finished the season with 9 goals in 45 matches in all competitions.

On 2 November 2019, Müller made his 500th competitive appearance for Bayern, becoming the 10th Bayern player to reach this mark since the club’s promotion to the Bundesliga in 1965. The following month, he became the first-ever player to register 11 assists in the first half of a Bundesliga season, achieving the new record in his side’s 2–0 win over Wolfsburg. On 7 April 2020, Müller pegged a contract extension keeping him at Bayern until 2023. He recorded his 20th assist of the Bundesliga season in an away match against Bayer Leverkusen on matchday 30, breaking the record for most assists in a season, previously held by Kevin De Bruyne and Emil Forsberg. He provided another assist in an away match against Wolfsburg on matchday 34, to finish off the season with a record of 21 assists.

On 5 March 2019, national team coach Joachim Löw confirmed that he would plan without Müller for the foreseeable future, along with his club teammates Jérôme Boateng and Mats Hummels. Müller said after the decision that he was “angry and surprised” why Löw decided to drop him and his Bayern teammates.

On 18 September 2020, Müller scored his first goal of the season, and provided one assist, in an 8–0 win over Schalke 04. He later managed to win the UEFA Super Cup and DFL-Supercup to be his 27th trophy of his club career; hence, he became the most decorated player in German history, breaking the previous record of 26 trophies won by his former Bayern teammate Bastian Schweinsteiger.