Mandzukic, who scored three goals for Croatia in the European championship, joined Wolfsburg in 2010 but despite scoring 12 goals in the recently completed season fell out of favour with coach Felix Magath.
"We are very happy to be getting a top Bundesliga striker with Mario Mandzukic, who showed his scoring abilities at the Euro," Bayern sports director Christian Nerlinger said.
Mandzukic is seen as another attacking option alongside Mario Gomez as Bayern plot how to wrestle the Bundesliga title off Borussia Dortmund, who have won German football's top competition the past two seasons.
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