The Italy international has been out of action since October 2011 after a recurring knee ligament injury which has needed two operations, but is expected to be back playing before the end of the season, and the striker believes he has chosen the right club to reignite his career at.
The former Manchester United player also revealed that he would have moved to the side in the summer had the opportunity arisen.
"I would have made this move sooner, even last summer," he told reporters at his unveiling.
"I’m happy to be at Fiorentina. They are the only side who came forward with facts and not just with words. That was very important to me.
"I like the Viola project a lot. I want to be a part of it. There are many youngsters here, but also players of experience. And we all know that Fiorentina are playing the best football in Italy.
"I can’t wait to start playing alongside Stevan Jovetic and Luca Toni. They are great players."
Rossi is predicted to be back in action in the spring, but the striker does not want to set a date for his return due to the fragility of his knee and the length of time that he has been absent from the game.
"I don’t have a particular date in mind for my return. My knee is stable right now, but it needs strengthening and it can’t be rushed," he said.
"I hope to get back to full fitness as soon as possible so that I can play for the Viola fans. Things are going well.
"Retiring? I’ve never thought about quitting. Being a footballer is the only thing that I know how to do."
The 25-year-old earned 27 international caps for Italy before his injury, and he admitted that once he is back to full fitness he would aim to return to the Azzurri.
He added: "The national team is certainly an objective, but I have to get fit before anything else. The key thing is that I get back to being 100 per cent."