The 25-year-old Japan international midfielder leaves Manchester United having failed to impress new manager Louis van Gaal.
Kagawa moved to Old Trafford in the summer of 2012 having spent two years in Germany where he collected back-to-back Bundesliga titles with Dortmund.
He also picked up a Premier League winners' medal at Old Trafford during Sir Alex Ferguson’s final season.
However, his only appearance for United this campaign was a 20-minute spell during their shambolic 4-0 Capital One Cup defeat to Milton Keynes Dons earlier this week.
Kagawa made 57 appearances for United, scoring six goals that included a hat-trick against Norwich.
He told Dortmund's official website: "I wanted to realise my Premier League dream but now I'm happy to be back in Dortmund.
"This great team, a unique environment and Dortmund is like a family. I am proud they have never forgotten me and I can belong again."
Dortmund’s sporting director Michael Zorc added: "The possibility of signing Shinji from Manchester United only arose for the first time in the last few days.
"Naturally we decided to add his enormous quality to our squad once again."
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