The Japan international failed to thrive at Old Trafford since his €22 million move from Signal Iduna Park to the Premier League two years ago and rumours have been rife all summer that he would be returning to the Bundesliga.
Dortmund confirmed the move for an undisclosed fee - reported to be €8m - with one day until the closing of the transfer window and BVB sporting director Michael Zorc admits the club leapt at the opportunity to bring the player back.
"The chance presented itself in the past few days to sign Kagawa from Manchester United for the first time ever," Zorc told the club's official website on Sunday. "Of course we opted to bring the enormous talent back to us to win more trophies."
"Shinji Kagawa is a technically gifted creative player who can determine the match in an instant," Watzke said.
"He wanted to return to Borussia Dortmund and we are sure that - given the right rest, time and appreciation - he will get back to the level he was at two years ago."
Kagawa, who follows in Nuri Sahin's footsteps as a player who has returned to Signal Iduna Park after a failed transfer abroad, is delighted to be back at last season's Bundesliga runners up.
"I already said on the day of my departure that the chapter Borussia Dortmund is not over for me," he said. "I wanted to make a dream come true by going to the Premier League.
"But now I am glad to be back in Dortmund with this great team, this unbelievable environment and these unique fans. BVB's like a family. I am proud they didn’t forget me and I can be part of it again."