The 24-year-old Romanian joins the club as cover for number one Joe Hart following the departure of Given to Villa Park.
Pantilimon made his senior international debut in 2008 and played against City twice in the Europa League last season, conceding three times.
Pantilimon, who was signed for an undisclosed fee, is expected to overtake Stuart Taylor and Gunnar Nielsen - City's other keeping options - to act as Hart's deputy.
Given joined Villa earlier this summer after losing his battle to displace the England goalkeeper.
Pantilimon is Roberto Mancini's fourth summer purchase, following left-back Gael Clichy from Arsenal, defender Stefan Savic from Partizan Belgrade and Argentina star Sergio Aguero, who arrived from Atletico Madrid in a deal worth around £38million.
Arsenal and Inter Milan had also been interested in the player, according to reports.
Manager Roberto Mancini hopes to bring in "another two or three players" before the transfer deadline at the end of the month.