Montenegro defender Stefan Savic, 21, has joined the Italian club as part of the deal, City said on their website.
Nastasic, 19, moved to Fiorentina from Partizan Belgrade in 2011 and quickly established himself in the back four, a rare bright spot in a disappointing season for the club.
He has twice been capped by Serbia, making his debut against Cyprus in February.
Savic made 11 appearances for City, scoring once in the 4-0 win over Blackburn Rovers in October.
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