The 25-year-old midfielder -- who played 71 games for United including 39 in the Premier League after moving there for 16million euros -- has signed a four year contract with the German giants, with whom he won the 2012 domestic double as well as the 2011 league title after he joined them for just 350,000 euros in 2010.

Kagawa, part of the Japanese squad that failed to fire at the World Cup finals, had looked to have a shaky future at United with their Dutch manager Louis van Gaal saying he did not fit his philosophy of football.

Kagawa made a promising start at United after being signed from Dortmund by Alex Ferguson in 2012 but injuries hampered his progress.

Kagawa hit out at Ferguson's successor David Moyes while on Japan duty after being consistently left on the bench last season and welcomed van Gaal's arrival, declaring his desire to fight for his place after a disappointing World Cup.

But the Dutchman recently made it clear the Japan playmaker's chances in his preferred role behind the strikers would be limited, prompting Kagawa to seek a move away.

Kagawa was not happy when van Gaal tried to convert him into a defensive midfielder during pre-season -- Angel di Maria's record 59million pound ($99million) arrival signalled the writing was on the wall for his future prospects.