The striker vowed to fight for his place following the announcement of the signing of Robert Lewandowski in January, but an exit became increasingly likely for the Croatian, who has admitted Bayern's style of play under Pep Guardiola does not suit him.
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"At Bayern it was fantastic. It's a fantastic club. Indeed, until recently I didn't even think about leaving, and especially that it would happen now," he told Sportske novosti.
"Let's be honest, the style Guardiola wants at Bayern doesn't suit me.
"In the first leg against Real in Madrid [in the Champions League semi-final], I definitely understood, no matter how much I try, I can't get the best out of myself with this style.
"When it's like that, I don't feel good and it's best for everyone that we part.
"Thanks to the club who offered a contract extension, thanks to Guardiola, who is a great coach, and I wish everyone all the best for the future.
"Bayern and their fans will always be the most beautiful and most emotional story of my career. The time has come for new challenges."
Mandzukic's contract at the Allianz Arena is currently set to expire in 2016.