United said the Everton manager was given a six-year deal and will take charge of the newly crowned Premier League champions from July 1.
Manchester United manager Alex Ferguson is retiring at the end of the season, bringing an end to more than 26 trophy-filled years at the club.
Manchester City missed the chance to put pressure on Premier League leader Manchester United on Saturday when it stumbled to a 3-3 draw against Sunderland that ended its record winning streak.
