Klinsmann is one of the most decorated of German footballers
Klinsmann will replace Ottmar Hitzfeld, who is due to step down from the post at the end of the current campaign.
The appointment marks Klinsmann's first foray into club coaching after he guided host nation Germany to third place at the 2006 World Cup.
He had been linked with the vacant Newcastle job and, earlier in the season, with Chelsea and Tottenham.
The 43-year-old was also viewed as a dark horse to succeed Steve McClaren as England national coach before the appointment of Fabio Capello.
606: DEBATE How good a coach is Klinsmann? There's not a lot on his CV
BBC Sport's Oliver Brett
He won 108 caps for his country. He scored 47 goals for Germany, 11 of which came in three World Cup campaigns.
Klinsmann featured in the 1990 World Cup-winning team and was then captain for the successful Euro 96 campaign.
He enjoyed a successful stint as a player with Bayern between 1995 and 1997, winning Uefa Cup and Bundesliga honours.
His managerial career is still in its infancy. After a period involved in Major League Soccer in the USA he returned to coach Germany in 2004.
The Bayern job is his first with a high-profile club.
Former German national coach Jürgen Klinsmann has been signed as the new Bayern Munich coach for the 2008/2009 Bundesliga season. This will mark Klinsmann's first managerial position at club level, succeeding current coach Ottmar Hitzfeld.

Over the past few months Klinsmann was being considered for various coach positions after reforming the German national team and finishing 3rd at the 2006 Football World Cup as coach of the German national team. Previously there had been reports that he was looking at Newcastle, Chelsea, Tottenham and there also was a possibility for him to be Steve McClaren's successor as the national coach for the English football team.

Klinsmann will be returning to the club where he played from 1995 till 1997 and won a UEFA Cup, a German league championship and a League Cup. Klinsmann's contract will start on July 1, 2008.