The former Arsenal captain won three Premier League titles before heading to Italy, but has now agreed to become Roberto Mancini's first signing since replacing Mark Hughes in the Eastlands hot-seat last month.
The 33-year-old midfielder has joined the Citizens on an initial contract until the end of the season with the option for a further 12 months should he impress on his return England.
Vieira was allowed to leave Inter on a free transfer as his contract was set to expire at the end of the season.
"Patrick is a world class midfielder with a winner's mentality and will fit into this group very well," 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."
Vieira is hoping the move back to England can revitalise he ambition to play for France in this summer's World Cup finals.