The 25-year-old joined City from Fiorentina for 22 million pounds ($34.4 million) in 2013 but has struggled to impose himself at the Etihad Stadium where his progress was hampered by injury.
"Everyone at City wishes Stevan well for his time with Inter," the club said in a statement on their website.
The Montenegrin netted 11 times in 44 games for City but never came close to living up to the standards he set in Italy despite occasional flashes of his ability.
A double in a 3-1 win over Liverpool at the start of last season was a rare bright spot in an otherwise difficult time at the club.
After the arrival of striker Wilfried Bony in January, Jovetic was left out of manager Manuel Pellegrini's Champions League squad, underlining his place in the pecking order at City, who have an embarrassment of attacking riches.
Following the 49 million-pound signing of Raheem Sterling, who was frequently deployed as a central striker for Liverpool last season, Jovetic's opportunities were always likely to be limited heading into the new campaign.
He leaves, however, having claimed the Premier League and League Cup trophies in his two years at the club.
($1 = 0.6392 pounds)
(Reporting by Toby Davis; editing by Ed Osmond)
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