Born in Tocopilla, Sánchez was a product of C.D. Cobreloa’s prolific youth ranks where he was teammate of current Chile national team players such as Charles Aránguiz and Eduardo Vargas. In February 2005, Sánchez was promoted to the senior first team by manager Nelson Acosta.

After an impressive season with Cobreloa, Sánchez caught the attention of Serie A club Udinese, which signed him for a £1.7 million fee, on 21 April 2006. Udinese, however, began a maturation project with Sánchez and immediately loaned him to Chilean giants Colo-Colo in a season-long deal.

Sánchez debuted for Colo-Colo on 23 June 2006 in a 1–1 draw with Antofagasta; he scored his first goal on 29 October during the Chilean football derby against Universidad de Chile in a 4–2 win. His good performances allowed him to break into the starting lineup after successfully challenging veteran striker Mario Cáceres, and he then began partnering Humberto Suazo in the forward position. On 1 November, he scored a brace in a 4–4 league draw against Deportes La Serena. as well as his first continental goal in a 7–2 thrash over Alajuelense from Costa Rica for the Copa Sudamericana. Nevertheless, Colo-Colo was runner-up of that tournament after losing the final against Pachuca of Mexico. On 23 December 2006, Sánchez won his first professional title after being starter in the Torneo Clausura final against Audax Italiano which his team won 3–2.

Sánchez made his international debut for the Chile national team against New Zealand on 27 April 2006. He was called up by the coach José Sulantay to represent the Chilean under-20 team at the 2007 FIFA U-20 World Cup held in Canada, where they finished third.

The next season, on 23 March 2007, he scored his first Copa Libertadores goals against Caracas at Cúcuta where he netted a hat-trick to a 4–0 away win. On 12 May, Sánchez scored his first and only one league goal during a 3–1 home win over Santiago Wanderers, key in the race for title with Universidad Católica which Colo-Colo finally reached after beat Palestino 1–0 at Monumental the last matchday. Noteworthy, it meant the club’s 26th league title.

After Sánchez’s impressive FIFA U-20 World Cup (where Chile achieved the third place with José Sulantay as coach), his loan with Colo-Colo expired and on 15 August 2007, he joined Argentina’s River Plate on loan from Udinese.

After his participation in the youth championship, Sánchez scored his first senior international goal in a 2–1 loss against Switzerland on 7 September 2007. He scored three times during La Roja’s successful 2010 FIFA World Cup qualification campaign and appeared on every match during the tournament finals. He then participated in the 2011 Copa América, scoring once in a 1–1 group stage draw with Uruguay, as Chile reached the quarter-finals. On 15 November 2013, Sánchez scored both goals as Chile beat England 2–0 at Wembley, repeating the achievement of national team legend Marcelo Salas in 1998.

After a successful season in Argentina, Sánchez left South America in July 2008 to join Udinese, where he would meet up with Chilean compatriot Mauricio Isla. Sánchez made his non-competitive debut in a 3–0 win over Bassano and was named the man of match. On 14 September, he played his first Serie A match in a 1–0 loss with Juventus and four days later, he made his European debut against Borussia Dortmund. On 19 October 2008, Sánchez scored his first league goal against Lecce. After this first goal, Sánchez got into a minor slump, in which he took much criticism. The criticism ended after scoring the winning goal in the 90th minute against Bologna in a 1–0 win, being named the man of match.

On 27 February 2011, Sánchez scored four of his team’s seven goals as Udinese comfortably defeated Palermo 7–0, playing only the first 52 minutes of the game. This event meant he broke the record of goals scored by a Chilean player (in a single match) in Serie A, beating the records set by countrymen Marcelo Salas and Iván Zamorano.

On 20 July 2011, Barcelona confirmed they had agreed to a €26 million fee (including €11.5 million in certain bonuses) with Udinese for the transfer of Sánchez, becoming the first Chilean to play for the club. “Sánchez is very young,” said then-manager Pep Guardiola; “He can play in all three attacking positions, he shows intense defensive skills, he’s direct and from what I’ve been told, he’s a very nice kid.” The transfer was finalised five days later when he passed a medical and signed a five-year contract. “I want to learn from players like Lionel Messi and Xavi Hernández—and I want to help the club win more titles,” said Sánchez.

Sánchez’s debut season for Barcelona was mired with short-term injuries. He made his debut on 14 August 2011 against archrivals Real Madrid in the 2011 Supercopa de España first leg away match, suffering a thigh injury after a challenge by Marcelo. Barcelona won the tie 5–4 on aggregate. He made his return two weeks later as a substitute in the 2011 UEFA Super Cup, won by Barca 2–0. Sánchez then started the opening match of La Liga, at home against Villarreal, and scored his first goal in a 5–0 win. A week later, on 10 September, he was stretchered off after 30 minutes following a challenge from Dani Estrada in a domestic league match against Real Sociedad. Sánchez returned on 1 November in an away match against Viktoria Plzeň. On 10 December, he scored Barça’s equaliser against Real Madrid in a match they went on to win 1–3 away at the Santiago Bernabéu Stadium. On 14 February 2012, Sánchez scored the first and second UEFA Champions League goals of his career in Barcelona’s 3–1 victory against Bayer Leverkusen.

In the 2012–13 campaign, on 2 October 2012 Sánchez scored the first goal for Barcelona in a 0–2 away win against Benfica. On 10 February 2013, then scored his first goal of the Liga season in Barça’s 6–1 home win against Getafe. From February onwards, Sánchez scored in matches against Deportivo de La Coruña, Mallorca, Athletic Bilbao, Real Betis, Atlético Madrid and Espanyol to end the season with eight league goals. Barcelona won the league title, ending the season with 100 points.

On 26 October 2013, Sánchez scored the winning goal as Barça beat Real Madrid 2–1 at Camp Nou in the first Clásico fixture of the 2013–14 La Liga season. On 5 January 2014, Sánchez scored his first hat-trick for Barcelona in a 4–0 win against Elche. He ended the 2013–14 season with a career-high 21 goals in all competitions, including 19 in La Liga.

On 10 July 2014, Sánchez signed for Arsenal on a long-term contract for a transfer fee of £31.7 million. Sánchez was given the squad number 17, previously worn by Nacho Monreal, who took the vacant number 18 instead. In a statement released by the club, Sánchez said that he was “so happy to be joining Arsenal, a club which has a great manager, a fantastic squad of players, huge support around the world and a great stadium in London”. Manager Arsène Wenger praised Sánchez, saying that the Chilean international “has consistently produced top-quality performances at the highest level for a number of seasons now and we are all excited to see him integrate into the Arsenal squad.” Sánchez made his first appearance for Arsenal on 2 August 2014, as a substitute during a 5–1 win against Benfica in the pre-season Emirates Cup tournament.

On 13 June 2014, Sánchez scored Chile’s opening goal of the 2014 World Cup, and provided an assist, in a 3–1 defeat of Australia in Cuiabá. During the round of 16, Sánchez scored the equalising goal in a 1–1 draw against the hosts Brazil. However, he was one of three Chileans to fail to convert their kicks in the penalty shoot-out, having his shot saved by Júlio César as Brazil prevailed 3–2.

Sánchez scored the first goal in Arsenal’s 2–1 home win over Queens Park Rangers on 26 December and assisted the second goal for Tomáš Rosický; earlier in the same match, Sánchez had a penalty saved by goalkeeper Robert Green after being brought down by Armand Traoré. On 4 January 2015, Sánchez scored and assisted his first ever FA Cup goals as Arsenal knocked out Hull City, the previous season’s runners-up in the third round. Sánchez assisted Per Mertesacker and scored in the 82nd minute, being substituted two minutes later by Chuba Akpom. In Arsenal’s next Premier League match, against Stoke City, Sánchez was involved in all the three goals as Arsenal beat the Potters 3–0 at the Emirates. He first assisted Laurent Koscielny and then scored two goals of his own. His performance was praised by Thierry Henry, who called him, “Arsenal’s best signing of the last six years.”

Sánchez reached his 25th goal of the season in the 2015 FA Cup Final on 30 May with the second goal in a 4–0 defeat of Aston Villa at Wembley Stadium, a long-range strike. Sánchez, who also headed an assist for Theo Walcott’s opening goal, became the first Chilean to score in an FA Cup final since Newcastle United’s George Robledo in 1952. He capped off his first season by winning Arsenal’s Player of the Year award.

On 26 September 2015, Sánchez ended a run of ten Premier League matches without a goal by scoring his first hat-trick for Arsenal in a 5–2 win at Leicester. This made him the first player to score hat-tricks in each of the Premier League, Serie A and La Liga. Sánchez then scored his first Champions League goal of the season a few days later, in a 3–2 loss to Olympiacos, latching onto a Theo Walcott cross to head beyond Olympiacos goalkeeper Roberto. The following league match, the last match before the international break, Sánchez scored for the third match in a row, scoring a brace in the first 20 minutes as Arsenal defeated Manchester United 3–0 at the Emirates Stadium and moved up to second place in the league. After the international break, Sánchez carried on his fine goalscoring form by netting against Watford at Vicarage Road, through a Mesut Özil assist, in a 3–0 Arsenal win, keeping Arsenal in second-place and grabbing his sixth goal in three Premier League matches for the club.

In Chile’s first match of 2018 World Cup qualification on 9 October 2015, Sánchez scored in a 2–0 win over Brazil, Chile’s first victory against the opponents since 2000. Four days later, he scored twice in a 4–3 win at rivals Peru.

In October 2015, Sánchez was named as a brand ambassador for Huawei.

Following a brief period on the sidelines due to injury, Sánchez returned to full first-team action on 30 January 2016 in the FA Cup fourth round tie against Burnley, scoring Arsenal’s second goal of the game following a low cross from Alex Oxlade-Chamberlain. Sánchez netted his first Premier League goal since October with a goal in the North London derby against rivals Tottenham Hotspur, equalising for Arsenal in the 76th minute and keeping the Gunners’ title challenge alive. During April 2016, Sánchez scored in four consecutive league matches, with goals against Watford, West Ham, Crystal Palace, and a brace against West Bromwich Albion.

When launching their new kit for the 2016–17 season, Arsenal announced that Sánchez will change squad number from 17 to 7, which was vacated by the departing Tomáš Rosický. Sánchez scored his first goal of Arsenal’s campaign and grabbed his first assist in Arsenal’s 3–1 away win over Watford. Sánchez scored his first Champions League goal of the campaign in a 1–1 draw with Paris Saint-Germain on 13 September 2016, latching onto Alex Iwobi’s rebounded shot, to secure Arsenal a point in the French capital. Sánchez kept up his spectacular run of form throughout September by netting against Hull, then scoring and assisting in a 3–0 victory over Chelsea. He scored a brace in a 1–4 win at Sunderland’s Stadium of Light, bringing his total to 50 goals in 106 appearances across all competitions for Arsenal. He also scored a hat trick and provided an assist in a man-of-the-match display in a 5–1 win at West Ham on 3 December. On 22 January 2017, Sánchez scored his first penalty for the club (having missed his previous two) against Burnley in an eventual 2–1 win, which put Arsenal into second place in the Premier League table. Sánchez scored his first goal in the season’s FA Cup, in a 5–0 quarter-final win over Lincoln City, taking his tally to 21 goals for the season in all competitions. Sánchez scored the winning goal in Arsenal’s 2–1 win over Manchester City, to send Arsenal through to their third FA Cup final, in four years.

In June 2016, Sánchez was part of the Chile squad that defended their Copa América title at the Copa América Centenario in the United States. On 14 June, needing a draw to progress to the knockout rounds, Chile fell 1–0 behind to Panama before both Sánchez and Eduardo Vargas scored twice in a 4–2 win in Philadelphia to qualify for the tournament quarter-finals.

On 13 April, Sánchez was included in the six player shortlist for the PFA Player of the Year. He also, in May 2017, won Arsenal’s Player of the Season award. Sánchez finished off the season by claiming the man-of-the-match award and scoring Arsenal’s opening goal in an eventual 2–1 win over Chelsea in the FA Cup Final, ensuring that Arsenal secured a record 13th FA Cup and that manager Arsène Wenger won a record 7th FA Cup in the process. He finished as the club’s top goalscorer with 24 Premier League goals, and 30 goals in all competitions, becoming the first player since Robin van Persie in 2011–12 to score more than 20 goals in the league.

Sánchez returned from the 2017 Confederations Cup with an injury, and therefore had to miss the team’s victory over Chelsea in the 2017 FA Community Shield and the team’s opening 4–3 win over Leicester City. Sánchez’ first start of the season came in the 4–0 away defeat to Liverpool. But throughout the transfer window, there was increasing speculation about his future, with a huge amount of reports stating his desire to leave, in order to play in the Champions League. A deadline day move to Manchester City was unsuccessful as Arsenal’s deal for Sánchez’s replacement Thomas Lemar was rejected. He scored his first goal for the season in Arsenal’s 3–1 UEFA Europa League victory over German side Köln, in which he picked the ball up outside the penalty area and curled a shot past goalkeeper Timo Horn, to score Arsenal’s second goal of the evening. Sánchez also played in Arsenal’s 1–0 win over Doncaster Rovers in the League Cup, in which Sánchez provided his first assist of the season, by delivering a cross-field pass which Theo Walcott subsequently put past Doncaster goalkeeper, Ian Lawlor.

In Chile’s opening match of the 2017 FIFA Confederations Cup on 18 June, Sánchez, who had been recovering from an ankle injury, came off the bench to set up Arturo Vidal’s opening goal in an eventual 2–0 win over Cameroon. On 22 June 2017, Sánchez became Chile’s out-right all-time goalscorer when he scored the opening goal in an eventual 1–1 draw against reigning World Cup champions Germany in his team’s second group match of the tournament, overtaking Marcelo Salas with his 38th international goal in 112 appearances, and also equalling Claudio Bravo as his nation’s joint top appearance holder in the process. Chile defeated Portugal on penalties in the semi-final, before losing 0–1 in the final against Germany, with Sánchez coming close to an equaliser with his injury time free kick saved by German goalkeeper Marc-André ter Stegen.

Sánchez had a statue erected in his honour within his native town of Tocopilla in March 2017.

In February 2017, Sánchez signed a sponsorship deal with Pepsi.

On 22 January 2018, it was announced that Sánchez had completed a transfer to Manchester United, in a swap deal that saw Henrikh Mkhitaryan move the opposite way. Sánchez was given the number 7 shirt. He made his debut for the club in a 4–0 victory against Yeovil Town in the fourth round of the FA Cup. He became the first Chilean to play a competitive match for United. He scored his first United goal on 3 February 2018 in a 2–0 home win against Huddersfield Town, after netting the rebound from his penalty, which had been saved by Jonas Lössl.

On 29 August 2019, Sánchez joined Inter Milan on loan for the duration of the 2019–20 season. He said he did not regret signing for Manchester United, but did wish he had played more.

On 14 September 2019, Sánchez made his debut for Inter when he came on as a 79th minute substitute in a 1–0 win against his former club, Udinese. On 28 September 2019, Sánchez scored his first Inter goal from a tap-in, before he was sent off after receiving a second yellow card for an apparent dive inside the box as the club won 3–1 against Sampdoria.

He was injured in October 2019 whilst on international duty with Chile.

On 6 August 2020, Sánchez made the permanent switch to Inter Milan, on a three-year deal, on a free transfer.