The 28-year-old says winning is his main priority at the Artemio Franchi, adding that Pep Guardiola was a big influence in his decision to join the Viola
The Germany international, who joined the Viola on a four-year deal, was part of Bayern’s treble-winning side last season.
And Gomez, 28, is targeting the club's first piece of silverware since lifting the Coppa Italia in 2001.
“My dream is to be able to win a title here in Italy,” he told reporters.
“Fiorentina made it clear they have ambitions in the league and want to take a step forward. They came fourth last year and want to be even more competitive in Serie A and also in Europe next season.
“I will not guarantee a certain number of goals. What matters is to score those needed for the team to get as many wins as possible.”
Gomez has spent the entirety of his career in Germany but began looking for a new club after falling out of favour at the Allianz Arena.
The striker admitted that Pep Guardiola, who recently took over at Bayern, influenced his decision to join Fiorentina.
"When it was clear that I had to leave Bayern, I had to decide between Spain and Italy," he continued.
“Nobody has convinced me to come. I only spoke with Guardiola who confirmed to me that Montella is a great person. And then I spoke with the club, who confirmed their objectives and the reasons why they wanted me here.
“Winning everything with Bayern was fantastic, but I want to experience something new. I spoke with Guardiola, who filled me in on how he was going to play. That is why I made this choice.”