Kagawa's time with United has come to an end after Borussia Dortmund signed their former player on a four-year deal.
"Of course we chose to sign this quality player again."
Since joining United in the summer of 2012 - signed by Sir Alex Ferguson - Kagawa struggled to reproduce the form he displayed in his first spell at Dortmund, which started when he joined them from Cerezo Osaka in 2010.
The 25-year-old made 57 appearances for United and scored six goals, including a hat-trick against Norwich, but failed to convince the club he was the playmaker they thought they had signed.
"I said on the day of my departure that my story with Borussia Dortmund was not completed," Kagawa told Dortmund's official website.
"I wanted to realise my Premier League dream but now I'm happy to be back in Dortmund; in this great team, the unique environment. Dortmund is like a family.
"I am proud they have never forgotten me and I can belong again."
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