The Montenegro international made the move as part of Matija Nastasic's transfer to Eastlands.
"Talking to Roberto Mancini I realised that I wouldn't have had enough playing time. Being young, my objective was to play consistently," revealed Savic.
"I made the right decision, especially as Serie A is one of the top Leagues in Europe. I don't think I'll have a problem settling in after playing in the Premier League.
"Stevan Jovetic's presence is very important for me in Florence, as we are international teammates and old friends.