Forlán has played for several South American clubs, including Argentine side Independiente, where he scored 37 goals in 80 league games. His goalscoring attracted the attention of European sides, and in January 2002, Independiente agreed a £6.9 million deal with Middlesbrough of the Premier League; the transfer fee would be paid over 18 installments. Forlán travelled to England expecting to negotiate with Middlesbrough, but at the last minute Manchester United gazumped the Teesside club, offering Independiente the same fee in a single payment, as well as a more lucrative salary for Forlán. On arriving in England, the Uruguayan negotiated with United officials for four hours, then informed the press of his decision. "Manchester United is a big club, so I've decided to go there," he explained. "The thing is, they offered more money than Middlesbrough." He signed for United soon after.
Forlán was signed for Manchester United by Sir Alex Ferguson for £6.9 million on 22 January 2002. He made his debut on 29 January as a 76th-minute substitute for Ole Gunnar Solskjær in a 4–0 away win at Bolton Wanderers. He made his first start in 4–0 home victory over Tottenham Hotspur on 6 March. Forlán made 13 Premier League and five UEFA Champions League appearances in the 2001–02 season but did not score.
On 18 September 2002, Forlán came on as a 56th-minute substitute for Ryan Giggs in a Champions League match versus Maccabi Haifa. He scored his first United goal as an 89th-minute penalty kick in the 5–2 win. His first Premier League goal was a 77th-minute equaliser in a home 1–1 draw against Aston Villa on 26 October. In Forlán's next Premier League game, at home to Southampton on 2 November, he came on as a 79th-minute substitute for United's goalscorer Phil Neville with the score at 1–1, and scored the winner with a dipping shot over Southampton goalkeeper Antti Niemi in the 85th minute. The goal also became notable due to his goal celebration where he ripped off his jersey, but then struggled to put it back on as the game recommenced, with Forlan making a blocked tackle while shirtless.
On 1 December, Forlan scored his first brace for Manchester United with goals in the 64th and 67th minute of an away 2–1 Premier League win at rivals Liverpool. On 17 December 2002, Forlán scored the winning goal as United defeated Chelsea in the quarter-finals of the Football League Cup. On 18 January 2003, Forlán scored a 90th-minute winning goal to again defeat Chelsea, this time in a Premier League match. Manchester United went on to win the Premier League title in 2002–03, and Forlán scored six goals to make him the club's third best-scoring striker that season after Ruud van Nistelrooy and Ole Gunnar Solskjær.
Forlán made his debut for Uruguay on 27 March 2002, scoring his first goal in a 3–2 friendly defeat against Saudi Arabia. During the 2002 World Cup, he scored a volley on 11 June 2002 in the group stage 3–3 draw against Senegal. Despite coming from three goals down to draw the game, Uruguay were eliminated from the tournament along with France in Group A. Diego Forlán and Youri Djorkaeff were, respectively, members of the Uruguay and France squads that met in the 2002 World Cup, in Group A. Their respective fathers, Pablo and Jean, featured in the match between Uruguay and France at the 1966 World Cup, which was also in Group A.