Klinsi is out of a job after the weekend defeat to Schalke, as Heynckes takes over at Bayern.
The official FC Bayern website states that the board, comprising Karl-Heinz Rummenigge, Uli Hoeness, and Karl Hopfner met this morning to communicate to Klinsmann that he was to be fired.
The former striker thus leaves Bayern after less than a year in charge, along with his assistants Martin Vasquez and Nick Theslof.
The website says that Klinsmann was ousted because he had failed to meet the minimum targets set for this season. Bayern are third in the Bundesliga, three points behind leaders Wolfsburg, and out of the Champions League.
Jupp Heynckes and Hermann Gerland will take over for the final five matches of the season, starting by taking the first team squad for training on Tuesday.
Klinsmann led the German national team to a third-place finish in the 2006 World Cup and was in line to take over as coach of the U.S. team following Bruce Arena's tenure.
However, the U.S. Soccer Federation and Klinsmann were unable to come to terms, and Klinsmann walked away from negotiations, opening the door to the Bob Bradley era.
Klinsmann is a long-time resident of Southern California who has played with local clubs (Orange County Blue Star) and on occasion advised young U.S. stars like Robbie Rogers on their soccer careers. He also invited Landon Donovan to join Bayern Munich on a short loan this winter, but declined to offer the Galaxy player a contract.
Ewan Macdonald, Goal.com