The Dutch midfielder will become the first non-German to wear the captain's armband.
"Mark is predestined for this role," Bayern coach Jurgen Klinsmann told the club's official website.
"He’s been an outstanding leader of the team since the start of pre-season, he radiates passion and isn’t afraid to voice criticism when he feels it is necessary."
Klinsmann has been contemplating appointing a new captain after former Germany keeper Kahn announced his retirement at the end of last season.
Van Bommel's language abilities played a major role in convincing Klinsmann assign him the duties of Bayern captain.
"He can communicate with the team in a number of languages," former Germany boss Klinsmann said.
Aside from his native Dutch, the 31-year-old Van Bommel speaks English, German and Spanish.