Klinsmann's fate was sealed after a meeting with club chairman Karl-Heinz Rummenigge, general manager Uli Hoeness and director Karl Hopfner on Monday morning.
First reported by Bild, Germany's mass-circulation tabloid, it momentarily displaced the negative headlines surrounding the club's president, former World Cup-winning forward Uli Hoeness.
Elsewhere, Bayern Munich striker Luca Toni looks set to depart the Allianz Arena in the near future after president Uli Hoeness confirmed he can leave the German Budesliga club.
Bosnia's Dzeko and Brazil's Grafite have scored 54 goals between them this season to break the previous record set by Bayern Munich's Gerd Muller and Uli Hoeness in the 1970s.
Landing Goetze marks the third time in three years the Bavarian club -- that Hoeness played an instrumental role in building on and off the pitch -- has lured a top transfer target from a fellow Bundesliga club.