The 21-year-old centre-back departed the Etihad Stadium to join the Viola on transfer deadline day, with teenage Serbian defender Matija Nastasic moving the other way.
Savic has no regrets about leaving City, where he made just 11 Premier League appearances last season, and is targeting success with his new club.
He said: "I have had few occasions to play for Manchester City and talking with coach (Roberto) Mancini I realised it was better for me to change team.
"I'm young and I need to play with continuity to grow. I think that Fiorentina is the right choice, also because Serie A is one of the best leagues in Europe.
"After playing in the Premier League, I should have not have a problem familiarising myself with Italian football.
"We are a good team and I think we can finish fifth or sixth in the Serie A table."
Source: team talk
Source: team talk