Kagawa, who scored 29 goals in 71 games during his first spell under Jurgen Klopp, found the back of the net just six times in 57 appearances for the Red Devils, and was subsequently moved on by new boss Louis Van Gaal.
He said: "The Premier League was a dream for me and I wanted to try and succeed there.
"However, now I am happy to be back at Dortmund with a great team, unique fans and fantastic surroundings.
"Being with Dortmund is like being with family."
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