The 23-year-old edged out Inter Milan's pacy full-back Yuto Nagatomo and Fulham goalkeeper Mark Schwarzer for the inaugural trophy, which is given to the best player based outside the AFC region.
A key player in Dortmund's league and cup "double" last season, Kagawa joined Manchester United for an initial fee of £12million during the summer amidst much fanfare.
He has shown glimpses of his mercurial ability for United this term but has not featured for Sir Alex Ferguson's men since the end of October due to a knee injury.
Ulsan Hyundai forward Lee Keun-ho won the AFC Player of the Year award for players based within the region.
The 27-year-old, who was briefly linked with Blackburn Rovers in 2009, was instrumental in leading Ulsan to the AFC Champions League title this season.