The 19-year-old, who can play at left back as well as centre back, was one of the revelations of last year's Serie A campaign, impressing many observers despite La Viola enduring an thorougly indifferent campaign.
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City boss Roberto Mancini will hope that Nastacic can build on his successful spell in Serie A and quickly establish himself in the first-team squad.
Nastacic was handed his Fiorentina debut by Sinisa Mihajlovic, a former assistant of Mancini during his time at Inter Milan, and the central defender did not take long to earn a permanent place in the first XI, as he went on to make 21 starts for the Florence club.
Savic bids farewell to the Etihad Stadium after failing to build on some initial promise. The 21-year-old joined the club from Paritzan Belgrade in 2011, and soon found himself thrown into the first-team setup due to a slew of injuries in the second half of the last campaign.
However, Savic, despite netting in a 4-0 win over Blackburn Rovers in October 2011, clearly did not do enough to convince Mancini that he would be capable of becoming an integral part of the City defence, and will now look to re-build his career in Italy.