Vieira becomes Mancini's first signing since replacing Mark Hughes last month.
Related ArticlesMan City and Arsenal help the agedMan City v Blackburn: previewVieira was interested in Spurs moveVieira can lift City to new levelVieira key to City aspirationsMan City Transfer TalkThe 33 year-old's deal at Inter was due to expire in the summer and the former AC Milan midfielder was keen to secure first-team football to work his way into the France squad ahead of the 2010 World Cup finals.
Mancini believes Vieira is the kind of player Manchester City require if the side are to challenge for a Champions League berth this season.
'Patrick is a world class midfielder with a winner's mentality and will fit into this group very well,' Mancini said.
'He knows me and my staff well, and importantly he also knows what the Premier League is all about. He will not need much time to settle in.
'Patrick is one of the great players of his era with 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.'
Vieira won three Premier League titles and lifted the FA Cup four times during his Arsenal days. He was also part of Arsene Wenger's 'Invincibles' that went unbeaten throughout the 2003-04 season.
During his time in Italy, Vieira won three league titles and two Italian Super Cups.
With France he won the World Cup in 1998 and European Championships in 2000.