Mandzukic completed his move to the Bavarian giants earlier this week.
“The first steps on Bavarian soil feel good. It is great to be here,” the 26-year-old told Bild.
“It’s not about names and transfer fees, only performance and quality,” Bayern Munich sporting director Christian Nerlinger told Bild.
“I am convinced that Mario is raring to go and totally focused on his new challenge at Bayern. His qualities were clear at the European Championships and they will be put to the test in the Bundesliga. We expect a lot from him.”
Everton, Tottenham, Aston Villa and Queens Park Rangers had all been linked with Mandzukic.