The defender, who transfers from Serbian side Partizan Belgrade, marks the second summer signing for the Blues after Gael Clichy joined earlier in the week.
“I can’t wait to play alongside [all the] fantastic players we have here," he told the club's official website. "It is a dream come true and I’m especially looking forward to meeting Edin Dzekoand Aleksandar Kolarov because they both speak my language and come from the Balkans, too.
“I watch the Premier League all the time and I know it’s the place to be so I am just looking forward to helping this club achieve great things. We have an incredible stadium and I’ve seen how passionate the City fans are many times on TV.”
The 20-year-old has earned six caps for Montenegro, who are level with groupmates England in the Euro 2012 qualifying round with 11 points.