He was left out of the squad for Bayern's 2-0 German Cup final win over Borussia Dortmund last month as his rift with former Barcelona manager Guardiola became apparent.
"I met with (Bayern chairman) Karl Heinz Rummenigge before the cup final and told him I wanted to leave the club," Mandzukic was quoted on Sunday as saying by Croatian daily Sportske Novosti.
"I've had a fantastic time at Bayern. It's a great club and I never thought I'd want to leave, and especially not at this point in time. But, let's be honest, I cannot play to my strengths under Guardiola's style no matter how hard I try.
"I realised that after the 1-0 defeat by Real Madrid in the Champions League semi-final first leg and, that being the case, it's best for all parties that we go our separate ways.
"Guardiola is an outstanding coach and I wish him and everyone else at the club all the best in the future.
"Bayern and the club's fans will remain the best and most emotional chapter in my career."
Mandzukic helped Bayern win an unprecedented treble for a German side in his first season at the club under Jupp Heynckes, scoring 22 goals in all competitions including the first in a 2-1 win over Dortmund in the 2013 Champions League final.
Despite improving his record under Guardiola to 26 goals in 48 games last season, rumours surfaced that the robust 28-year-old hitman felt uncomfortable playing the Spaniard's Barca-bred tiki-taka style based on keeping possession.
The system won Guardiola a haul of trophies at Barcelona but backfired spectacularly in the Champions League semi-final return, which Real won 4-0 before lifting a 10th European Cup with a 4-1 win over city rivals Atletico in Lisbon last month.
Mandzukic will miss the opening match of the World Cup for Croatia against hosts Brazil on Thursday through suspension after he was sent off in the second leg of November's 2-0 aggregate playoff win over Iceland.
His striking qualities will undoubtedly be welcome wherever he moves after the finals but he was staying tight-lipped on his likely destination.
"It's time for a fresh challenge but don't insist because I have nothing to say. The public will be informed when the time comes; right now I am focused solely on the World Cup."
- Sports & Recreation
- Borussia Dortmund
- Karl Heinz Rummenigge