The 33-year-old French midfielder has joined the City on a free transfer from Inter Milan and has signed an initial contract until the end of the season with the option for a further 12 months should he impress at Eastlands.
"Patrick is a world class midfielder with a winner's mentality and will fit into this group very well," City boss Roberto Mancini told the club's official website.
"Patrick is one of the great players of his era with every almost every honour in the game against his name.
"I am sure City fans will welcome him warmly and appreciate the contribution he will make."