The 27-year-old Germany international is understood to be on the verge of signing a four-year contract at the Stadio Artemio Franchi after scoring 112 goals in over four seasons with the Bundesliga champions.
Bayern chairman Karl-Heinz Rummenigge told his club's official website, fcbayern.de: "Mario Gomez wanted to leave Bayern Munich and go to Florence. We have now complied with his wishes."
Gomez joined Bayern from Stuttgart in 2009 for a reported 30million euros - at the time the Bundesliga's record transfer fee - and his consistent prowess in front of goal helped bring two league titles, two German Cups and the Champions League to Munich.
"With those goals, he made a big contribution to winning two Bundesliga titles and two DFB-Pokal triumphs," Rummenigge added.
"The highlight was, of course, the Champions League triumph and the treble last season. I would like to thank him for his efforts for Bayern.
"On behalf of FC Bayern, I wish him lots of happiness and success in Florence."
Gomez was the Bundesliga's top goalscorer in 2011, notching 28 times, but after missing the first part of the 2012-13 season due to injury he struggled to return to the Bayern first team and found himself behind Mario Mandzukic in the pecking order.
With the prospect of that situation enduring under new Bayern coach Pep Guardiola this season, he requested a transfer and set his stall on a move to Fiorentina, who had finished fourth in Serie A under ambitious coach Vincenzo Montella.
After initially struggling to reach Bayern's asking price, the Viola have now reached a compromise to make Gomez their second high-profile signing of the summer following the arrival of former AC Milan midfielder Massimo Ambrosini.
Gomez is expected to form a three-man trident alongside Giuseppe Rossi and Stevan Jovetic - should the in-demand Montenegrin remain in Tuscany - while the Viola boast an impressive range of creative options in a midfield that includes Adem Ljajic, Borja Valero, Alberto Aquilani and David Pizarro.