The Bavarians have lost Ivica Olic this summer, and although the club re-signed Claudio Pizarro, it was also linked with a move for Manchester City's Edin Dzeko.
However, Bayern was priced out of a move for the Bosnian, and turned its attention to the Croatian, who scored three goals at Euro 2012.
Speaking to the club's general manager Christian Nerlinger admitted that the 26-year-old's performances in the tournament were a factor behind the move, along with his consistent performances at club level.
"We are delighted to bring a top Bundesliga striker like Mario Mandzukic, and we have also seen in Euro 2012 matches that he has special skills," the 39-year-old told the club's official website. "He will continue to strengthen our squad."
Mandzukic moved to the Bundesliga from Dinamo Zagreb in 2010, and is Bayern's third summer signing alongside Pizarro, and former Borussia Monchengladbach defender Dante.
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