The German international sealed his move from Bayern Munich last week, and wants to bring a winning mentality to the club.
He has refused to set a goal target but is excited by his move.
"My dream is to be able to win the title here in Italy," Gomez told reporters.
"Fiorentina made it clear that 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."
Reports emerged today that Fiorentina will also be selling a striker, after agreeing a fee with Manchester City for Stevan Jovetic.