"Captain Mark van Bommel is joining AC Milan effective immediately," Bayern said in a statement. "The Dutch international asked for his contract to become void to transfer for sporting reasons."
The 33-year-old midfielder has signed a short-term deal until June, injury-hit Milan said on their website.
The Dutch international, who joined Bayern from Barcelona in 2006 after winning the Champions League, had dropped down the pecking order under coach Louis van Gaal with the arrival of Brazilian Luiz Gustavo in January further hampering his chances.
"I leave Bayern with a heavy heart but my head held high," said Van Bommel, who won two German championships and Cups and reached last year's Champions League final before playing at the World Cup where Netherlands reached the final.
"I spent four-and-a-half happy and successful years (at Bayern) and would like to thank the club and the fans. Bayern will always occupy a big place in my heart," he said.
Milan are hoping he will provide some solutions to their injury crisis in midfield although Van Bommel is ineligible to play for the Italians in this season's Champions League having already featured for Bayern in the group stage.
"It was Mark's specific request to release him from his contract so he can transfer for sporting reasons," said Bayern CEO Karl-Heinz Rummenigge.
"Mark was always an exemplary professional, an important and successful player. Based on those achievements we granted his wish," he said.
The Italian side have midfielders Andrea Pirlo, Kevin-Prince Boateng, Clarence Seedorf and Gennaro Gattuso among others injured although they signed left wing-back Urby Emanuelson from Ajax Amsterdam on Sunday. He is also ineligible for this season's Champions League.
Milan, who have said they are interested in Genoa's Italy left-back Domenico Criscito, face Tottenham Hotspur in the last 16 next month.
