The 24-year-old – who won the Premier League title with Manchester City in 2012 – has signed a five-year contract for a fee reported to be around nine million euros by Italian media.
“We are delighted over this agreement with Fiorentina, because Stefan is a very promising player with a great future ahead of him,” said Atletico sporting director Jose Luiz Perez Caminero.
“He is a quick and potent defender, with experience beyond his youth, having played in the top leagues of Serbia, England and Italy. I am convinced that he will contribute greatly to the team.”
Savic, who had been with Fiorentina since 2012, will fill the void left by Brazilian international Joao Miranda’s departure to Inter Milan.
The Spanish press report that, as part of the deal, Atletico midfielder Mario Suarez will move the opposite way.
Suarez made 11 league starts for Atletico last season and is willing to leave the Rojiblancos in search of more playing time.
Savic believes Suarez will be an important signing for Fiorentina.
“Suarez is a great player,” he said. “He is going to Fiorentina and I’m sure that he will help them achieve success.”