"I've come to know myself and my personality over the last three, four years on the coach's bench", Vieira said.
"I can honestly say that my time with the club has been absolutely ideal - both on the professional and personal level".
Vieira led New York City to two consecutive playoff appearances and leaves with the team in second place in the Eastern Conference.
In a statement announcing the hiring, the Riveira club had said they were "looking for a coach with the ability to continue to play flowing football, bring on young players and take the risk of having them evolve while bringing a winning spirit to the table. We know that leaving the club has been a hard decision for him, but we understand his choice to return to Europe where he spent his whole playing career", team vice chairman Marty Edelman said.
Arsenal and Marseille are just two of the sides keen, but new Nice coach Vieira has no wish to see Balotelli walk out of the exit door.
"I know we have a very talented team, I have watched numerous matches and I enjoy the way the team plays and I now can't wait to begin working with the players on the training pitch", the Catalan said in a release.
"A smooth transition was certainly a priority, particularly for a group of players who have had an excellent campaign so far", he said.
Vieira played 107 times for France and was part of the squads that won the World Cup and Euro 2000.