Klinsmann, who was assisted by Low when he led the national team to third place in the 2006 World Cup, will take over from Ottmar Hitzfeld at Bayern at the end of the season.
Low admitted he had not seen the move coming, saying: "It does come as a bit of a surprise. He is a true ambassador for German football. It is an exciting project for a former national team manager, who achieved a lot, to coach a top German club."
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