Bayern have beaten Real Madrid, Arsenal and Lyon in the race to sign Ribery, despite the club’s failure to qualify for next season’s Champions League.
Ribery have signed a four-year contract with the German giants.
Olympique Marseille chairman Pape Diouf told the club’s Web site: “We have helped Franck to get where he is today and we are not really happy to let him go.
“It’s a good financial operation for the club, which proves Marseille can adapt to a market that is not easy.”
Bayern will have to pay a 26.0 million euro transfer fee and then an additional 4.0 million if the German side manage to qualify for the Champions League at the end of next season.