Morata signed for Real Madrid in 2008 from neighbouring Getafe after starting out at Atlético Madrid, and appeared for Real Madrid C while still a junior. In July 2010, after a successful season with the Juvenil A team, where he won two youth titles and scored 34 goals, he was promoted to Real Madrid Castilla, Real’s reserve team. Later that month, first-team manager José Mourinho took Morata and four of his teammates on a preseason tour in the United States.

On 15 August 2010, Morata made his debut with Castilla in a friendly match with Alcorcón, scoring the only goal of the game. His Segunda División B debut came on 29 August in a 3–2 win against Coruxo, and he scored his first competitive goal in a 1–1 draw against Alcalá on 31 October.

On 12 December 2010, Morata made his debut for the first team when he was brought on as a substitute for Ángel Di María in the 88th minute of a 3–1 La Liga win at Real Zaragoza. Ten days later he made his first appearance in the Copa del Rey, again coming off the bench in the last few minutes. In January 2011, after Gonzalo Higuaín’s injury, the Spanish media expected Morata to be his replacement in the main squad. Mourinho, however, rejected this, saying that “Morata is not yet ready to be a starter at Madrid. He trains with us, but he has to continue learning with Castilla”. In this period Morata scored five goals in four matches with the reserves, while Emmanuel Adebayor was signed to replace Higuaín in the first team.

On 13 February 2011, Morata scored the first hat-trick of his career, in a 7–1 victory against Deportivo Fabril. He finished his first season as a senior with 14 league goals – joint top scorer in the squad with Joselu – but Castilla failed to gain promotion in the play-offs.

Morata scored his first competitive goal with Real’s first team on 11 November 2012, coming on in the 83rd minute and scoring the winner after just 60 seconds in a 2–1 away win against Levante. In his first official start, at home against Rayo Vallecano on 17 February of the following year, he scored the opener after just three minutes, but was substituted before the half-hour mark to make room for Raúl Albiol, after Sergio Ramos was sent off in a 2–0 home victory.

On 2 March 2013, Morata played the full 90 minutes of El Clásico against Barcelona, assisting Karim Benzema to score the opener in an eventual 2–1 home win. In the following season, he became a regular member of the first-team squad under new coach Carlo Ancelotti, but expressed a desire for more minutes during the January transfer window.

On 18 March 2014, Morata scored his first goal in the UEFA Champions League, the third goal in a 3–1 win over Schalke 04 at the Santiago Bernabéu in the round of 16. On 17 May, in the last game of the league campaign, he scored two late goals against Espanyol to help Real to a 3–1 home win, and finish with eight goals in the competition. He also featured in the club’s victory in the UEFA Champions League Final against Atlético Madrid, playing the last ten minutes of regular time and extra time after replacing Benzema.

On 19 July 2014, Juventus announced that they had reached an agreement for the fee of €20 million for the transfer of Morata, who signed a five-year deal, with Real Madrid having the option to buy him back in the future. He made his debut in Serie A on 13 September, replacing Fernando Llorente for the final minute of a 2–0 home win against Udinese; two weeks later he again came on in place of his compatriot, and headed his first goal for his new club as they won 3–0 at Atalanta.

On 5 October 2014, in a 3–2 home win against Roma, Morata came on as a substitute and was sent off for a foul on Kostas Manolas, who was ordered off for retaliating. On 9 November he scored twice in a 7–0 home demolition of Parma, with Llorente – whom he replaced after 71 minutes – adding a further two. Morata came on for the final ten minutes of the Supercoppa Italiana against Napoli in Doha, Qatar on 22 December, and scored in the penalty shoot-out which Juventus lost 5–6.

On 7 November 2014, Morata was called up to manager Vicente del Bosque’s senior squad for matches against Belarus and Germany. He made his debut against Belarus on the 15th, replacing Isco for the last ten minutes of a 3–0 win in Huelva for the UEFA Euro 2016 qualifiers. In the same competition, on 27 March 2015, he scored his first senior international goal, the only goal in a victory over Ukraine in Seville.

In March 2014, Morata shaved off all of his hair in solidarity with sick children, saying “kids with cancer wanted to have my haircut but they couldn’t, so I gave myself theirs”.

On 28 January 2015, Morata played the last 13 minutes of the Coppa Italia fixture against Parma, and scored the game’s only goal at the Stadio Ennio Tardini to qualify for the semi-finals. The following month, at home against Borussia Dortmund in the UEFA Champions League round of 16, he scored the winner in the 43rd minute of the first leg; he also started and found the net in the return match, helping Juve to a 3–0 win at the Westfalenstadion.

On 7 April 2015, Morata was sent off for a foul on Alessandro Diamanti as Juventus defeated Fiorentina in the cup semi-final, thus missing the final. One week later, he won a penalty in the first leg of the Champions League quarter-final against Monaco, which was converted by Arturo Vidal in a 1–0 home win. In the first leg of the semi-final, against Real Madrid, he put the hosts ahead with a tap-in in the eighth minute, as the match ended in a 2–1 home victory, and he repeated the feat in the return match, on both occasions not celebrating scoring against his former club. On 6 June, in the final against Barcelona in Berlin, he scored the equaliser early in the second half of a 1–3 loss.

On 10 December 2015, Morata signed a contract extension until 2020. On 20 March 2016, in the Derby della Mole away to neighbours Torino, he came off the bench in the first half and scored twice in a 4–1 victory. On 21 May, he again came off the bench to score the winning goal in the 20th minute of extra time to win the Coppa Italia final 1–0 against A.C. Milan in Rome’s Stadio Olimpico.

On 21 June 2016, Real Madrid exercised their buy-back clause to re-sign Morata from Juventus for €30 million. His first competitive appearance was on 9 August, as he started in a 3–2 win over fellow Spaniards Sevilla in the 2016 UEFA Super Cup, being replaced by Benzema after 62 minutes. His first goal came in a 2–1 home win over Celta on 27 August.

On 10 December 2016, he got engaged to his Italian girlfriend Alice Campello, and on 17 June 2017, the pair were married in Venice. The two welcomed twin sons Alessandro and Leonardo on 29 July 2018, and the player changed his kit number at Chelsea from 9 to 29 to honour them. On 29 September 2020, the couple’s third son, Edoardo, was born.

On 5 April 2017, Morata profited from manager Zinedine Zidane’s rotations and scored three times in a 4–2 away win against Leganés to keep his team two points clear of Barcelona with a game in hand. In spite of spending the vast majority of the season as backup to Benzema, he scored 15 league goals as the club was crowned champions for the first time in five years. He added three goals in nine appearances in the UEFA Champions League, which Real Madrid won for the second successive year.

On 19 July 2017, Chelsea announced that they had agreed terms with Real Madrid for the transfer of Morata, for a reported club-record fee of around £60 million. On 21 July, he successfully passed his medical and officially became a Chelsea player.

Morata made his competitive debut in the 2017 FA Community Shield match against Arsenal, coming on as a substitute in the 74th minute as his team lost on penalties after drawing 1–1 in normal time, with Morata missing in the shoot-out. On 12 August 2017, he scored and provided an assist for David Luiz in his first appearance in the Premier League, a 2–3 defeat at home to Burnley – his goal was a header in the 69th minute of the game to cut the deficit to 3–1. On 23 September, he scored his first hat-trick for Chelsea in a 4–0 away win against Stoke City; this made him the 17th Chelsea player to score a hat-trick in the Premier League.

On 5 November 2017, Morata scored in the 1–0 home defeat of Manchester United, coached by his former boss Mourinho. He took his league tally to ten goals on 26 December, helping Chelsea to a 2–0 win over Brighton & Hove Albion, also at Stamford Bridge.

Selected for the finals in France, Morata started and scored a brace in a 3–0 group win against Turkey in Nice. On 2 September 2017, coming off the bench in the 77th minute, he scored once to help the hosts defeat Italy 3–0 in the 2018 FIFA World Cup qualifiers.

On 17 January 2018, Morata was sent off after picking up a booking for diving, then another seconds later for dissent, in a third round FA Cup replay win over Norwich City. He finished his first year with 15 goals in all competitions, and the Blues finished fifth in the league table.

Morata opened his account for the following campaign on 18 August 2018, scoring the second goal in a 3–2 home victory against Arsenal. On 4 October, he scored the winner in a 1–0 win over MOL Vidi in the group stage of the UEFA Europa League. A month later, he scored twice to help beat Crystal Palace 3–1 in a league fixture at home.

On 21 May 2018, Morata was left out of Spain’s World Cup finals squad after a poor club season.

On 27 January 2019, Morata returned to Atlético Madrid after 12 years, joining the club on an 18-month loan deal. He made his league debut on 3 February, in a 0–1 away loss against Real Betis. He scored his first goal on 24 February, in a 2–0 home win over Villarreal.

On 6 July 2019, Atlético Madrid confirmed the permanent signing of Morata from Chelsea and he would officially join the club on 1 July 2020, for a fee around £58 million.

On 18 August 2019, Morata scored the only goal in Atlético Madrid’s La Liga opener win against Getafe. On 1 October 2019, Morata marked his 300th professional game with an assist for the game’s opening goal in a 2–0 away win against Russian side Lokomotiv Moscow. On 22 October, he scored his first Champions League goal for Atlético by heading home Renan Lodi’s cross for the only goal of the game in a 1–0 win at home against German side Bayer Leverkusen. This also made him the first player to score for both Real Madrid and Atlético in the Champions League. On 11 March 2020, in the Champions League last 16 second leg away to defending champions Liverpool, Morata came on as a late substitute in extra time and scored the final goal of the game in a 3–2 away win, thus winning the tie 4–2 on aggregate, ensuring his team’s qualification to the quarter-finals of the competition.

Morata returned to Juventus on 22 September 2020, on a one-year loan worth €10 million, with an option for purchase at €45 million. Juventus also reserve the right to extend the loan for a further year for another €10 million; in this case, the option for purchase is worth €35 million. He made his first appearance for the club since his return on 27 September, in a 2–2 away draw against Roma in Serie A. He scored his first goal for the club since his return on 17 October, in a 1–1 away draw to Crotone. Morata scored a brace on 20 October, to help Juventus win 2–0 in the UEFA Champions League group stage match against Dynamo Kyiv away from home. On 28 October, he had three goals disallowed for offside against Barcelona in a Champions League group stage game, which Juventus lost 2–0 at home.