The 20-year-old has been granted a work permit by the Home Office and becomes City's second signing in three days following the arrival of Gael Clichy from Arsenal.
He moves to the Premier League 12 months after a trial period with the Gunners ended without Arsene Wenger declaring an interest.
At the time, it was thought Savic would only have cost the Gunners ?2million. That City might be paying up to five times that sum indicates how well Savic has performed both for Partizan Belgrade, who won the Serbian title last term, and Montenegro, who have rocketed up the FIFA rankings and represent the greatest threat to England's hopes of automatic qualification for Euro 2012.
Indeed, when the two countries fought out a goalless draw at Wembley in October, Savic came face to face with five current City players.
"I never imagined that I'd be team-mates with all those City players within a year," he told www.mcfc.co.uk.
"I can't wait to play alongside them and all the other fantastic players we have here.
"Montenegro play England later this year so I am expecting to have some great banter with the England lads."
Source: Team Talk
Source: Team Talk