Bayern chairman Karl-Heinz Rummenigge concluded the deal, confirming Gomez had asked to leave the club.
He said in a statement on the Bayern website: "It was Mario Gomez’ desire to leave Bayern and join Fiorentina. We've now accommodated his wishes."
Gomez enjoyed a very successful four-year stint at the club after joining from Stuttgart in 2009 - becoming the Bundesliga's most expensive signing at the time.
He scored a remarkable 112 goals in 172 appearances for the German side, while finishing top scorer in the Bundesliga in 2011.
He also played his part in Munich winning the European Cup, Bundesliga and the German Cup treble last season.
Despite this Gomez only started nine Bundesliga games last season, so the chance of regular football in Italy may well have swayed the German striker's mind when deciding to leave Bayern.
Rummenigge reserved special praise for the German striker, thanking him for his huge contribution to the club's continued success over the last four years.
He made a major contribution to two German titles and and two German Cup wins," added Rummenigge. "The highlight, of course, was the Champions League win and the treble last season.
"I want to thank him for his performances for Bayern. On behalf of the club I wish him lots of luck and success in Florence."
Gomez's new club Fiorentina finished fourth in Serie A last season to qualify for the play-off round of the Europa League.
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