The former Arsenal player, 33, is Roberto Mancini's first signing since taking over as coach at City last month.
"Patrick is a world class midfielder with a winner's mentality and will fit into this group very well," Mancini told the City website.
"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."
"I am really confident and I believe in myself. I know I am not 20 but I am not 40 or 45. I am still motivated," Vieira told reporters.
"We can achieve something really special here. I want to convince the City board and the City players and fans that I didn't come here just to spend six months."
"I have come here to give something to the club. I believe that I still have a lot to give and I believe the team is strong enough to win trophies."
Vieira moves in search of regular first-team action in a bid to win a place in the France squad for June's World Cup finals in South Africa, a move Les Bleus manager Raymond Domenech has welcomed.
"If he plays and if he plays at his true level, there is no reason why he shouldn't come to South Africa," Domenech told the French sports daily L'Equipe.
Vieira, whose contract at Serie A leaders Inter was due to expire at the end of the season, made his final appearance in Wednesday's 1-0 win at Chievo Verona.
"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," Mancini said.
"(I will approach the match) the same way that I will against all the other teams," he said.
Arsenal manager Arsene Wenger, who signed Vieira in 1996 told Sky Sports: "For me has had made the right choice, City have made the right choice - it should be a good marriage."
NEWS: Redknapp - I snubbed Vieira swoop
NEWS: Domenech offers Vieira World Cup hope
Follow FFT.com on Twitter
Join FFT.com on
