Vieira, who spent two-and-a-half years in charge of NYCFC, replaces Roy Hodgson, who stepped down at the end of last season.
“I am really excited to have this opportunity to return to the Premier League, and manage this great football club, as we begin a new chapter together,” Vieira said in a club statement. “It is a project that is really appealing to me, having spoken a lot with the Chairman and Sporting Director about their ambition and plans for the whole club, including the Academy. The club has fantastic foundations in place after many years in the Premier League, and I hope we can make further improvements and continue to drive the club forward.”