The 24-year-old -- who won the English Premier League title with Manchester City in 2012 -- signed a five year contract for a fee reported to be around 9million euros ($9.7million) 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 pacey and powerful defender, and is experienced despite his youth."
Savic, who had been with Fiorentina since 2012, will fill the vacuum left by Brazilian international Joao Miranda's departure to Inter Milan.