The 26-year-old will join the Bavarians on a four-year contract pending a medical which should take place in Munich in the coming days.
Mandzukic scored 20 goals in 56 appearances for Wolfsburg since joining them from Dinamo Zagreb in 2010. He also netted three times in three games for Croatia at Euro 2012.
"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 is the sixth new arrival in Munich this summer, following Xherdan Shaqiri, Dante, Tom Starke, Claudio Pizarro and Mitchell Weiser.