Mandzukic has been linked with a host of Premier League clubs, including Chelsea, after his future with the Bundesliga giants became unclear.
The 28-year-old striker has confirmed he is leaving Bayern, mainly due to coach Guardiola's possession-based style not suiting his game.
Mandzukic also revealed he had a meeting with Karl-Heinz Rummenigge in early May, telling the Bayern chief he wanted a move.
"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 UEFA Champions League), 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 refused to say where his next challenge would be as he prepares to represent Croatia at the FIFA World Cup.
He is suspended for Thursday's tournament opener against Brazil, but is sure to face Cameroon and Mexico in Group A.
