The 26-year-old has signed a four-year contract with Bayern and joins the club for an undisclosed fee.

"We are very pleased to have signed Mario Mandzukic, who is one of the top strikers in the Bundesliga who proved his goalscoring qualities at Euro 2012 in Poland and Ukraine," said Bayern's director of sport Christian Nerlinger.

"He will bring further strength to our squad."

Mandzukic scored 20 goals in 56 appearances for Wolfsburg since joining them in 2010.