The 18-year-old was signed from Partizan Belgrade in January, but could not make the move until now due to the limit on non-EU players.
"I had a very warm welcome in Florence, especially as there are quite a few Serbs in the squad," he said at his presentation Press conference.
"I've been following Italian football for a long time and I'm ready for this challenge."
Nastasic joins the Viola and is already looking forward to the toughest possible tests.
"I know how to move and I really want to mark Ibrahimovic. I'm a left-footed centre-back and my idol is Nemanja Vidic, but when he was still playing, Sinisa Mihajlovic was my hero."