The Bundesliga club announced that the Japan international midfielder had rejoined them on Sunday afternoon, ending a two-year stay at Old Trafford.
"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."
Kagawa has been restricted to just one appearance under new United manager Louis van Gaal this season, coming in their 4-0 Capital One Cup defeat against Milton Keynes Dons.
United had still to confirm Kagawa's departure but its impact is unlikely to be felt in the wake of Angel di Maria's recent arrival.
THE VIEW FROM GERMANY
Daniel Rathjen, Eurosport.de: "After the transfers of Goetze und Lewandowski to Bayern Munich, fans of BVB were full of frustration and anger. Therefore the retun of the "lost son" Kagawa is heartwarming for them.
"The feeling they have right now is nearly similar to how they felt when Nuri Sahin found his way home. Both are loved and admired in Dortmund.
"But: All should keep in mind that this actually is 2014 - and not 2012 anymore. BVB has evolved without Kagawa. In the current team he is no longer the outstanding player.
"With Mkhitaryan and Reus there is strong competition. Sahin also felt this when he returned among the likes of Ilkay Gundogan.
"In principle the transfer of Kagawa makes sense for both sides. Borussi-"SPA" Dortmund may be the only place where he can regain his strength!"
- Sports & Recreation
- Shinji Kagawa
- Borussia Dortmund
- Manchester United