On 28 January 2012, Kagawa scored twice in Dortmund's 3–1 win against Hoffenheim. Kagawa scored the only goal of the game against Werder Bremen on 17 March, heading in a pass from İlkay Gündoğan in the eighth minute. Kagawa scored two goals in Dortmund's 6–1 thrashing of Cologne on 25 March, keeping Dortmund five points ahead of Bayern in the title race. Kagawa won the Bundesliga with Borussia Dortmund in 2012 as they set a Bundesliga record scoring the most points in a season in the Bundesliga, with 81. Kagawa also scored a goal and provided an assist for Dortmund against rivals Bayern Munich in the 2012 DFB-Pokal Final. He scored a total of 13 goals and had 8 assists during that season.
On 5 June 2012, it was announced by Manchester United that the club had reached an agreement with Borussia Dortmund and Kagawa for his transfer, a deal that made him the first Japanese player to join the club. The fee was reported to be an initial £12 million, with a further £5 million in possible add-ons. The transfer was completed on 22 June after Kagawa passed his medical at Manchester United and received his UK work permit. On 3 July, it was revealed that Kagawa would wear the number 26 shirt for United. Kagawa spoke about his former club, Borussia Dortmund, saying, "I will carry this club, their great fans, and the whole city in my heart forever and will follow their results with great interest."
On 18 July 2012, Kagawa was handed a two-minute appearance to mark his Manchester United debut in Durban, South Africa, against AmaZulu in a pre-season friendly match. Kagawa made his first start for the Red Devils against Ajax Cape Town on 21 July 2012, and scored his first goal against Shanghai Shenhua four days later. He made his Premier League debut on 20 August 2012, playing the full 90 minutes of United's 1–0 defeat away to Everton. He scored his first goal against Fulham on 25 August in his home debut for the club. After Tom Cleverley's shot was parried by Fulham goalkeeper Mark Schwarzer, Kagawa scored on the rebound from close range. On 19 September, Kagawa was given his first Champions League start as United played against Galatasaray. He provided an assist for the winning goal scored by Michael Carrick in a 1–0 win. On 23 October, he set up Javier Hernández for United's first goal in an eventual 3–2 Champions League victory against Braga. In that match, however, he twisted his knee, which left him sidelined for two months. Kagawa returned from injury in January 2013.