The 26-year-old is moving to the Allianz Arena on a four-year contract, and is the club's third summer signing after Dante and Claudio Pizarro
The Bavarians have lost Ivica Olic this summer, and although they have re-signed Claudio Pizarro, they were also linked with a move for Manchester City's Edin Dzeko.
However, they were priced out of a move for the Bosnian, and turned their attention to the Croatia international, who scored three goals at Euro 2012.
Bayern 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 for Wolfsburg last season.
"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.