The 50-year-old has signed a six-year-contract with the Old Trafford outfit and will join officially on July 1 after completing the season with Everton.
Moyes has the backing of Sir Alex Ferguson, who confirmed his retirement on Wednesday, and his first official game will be the Community Shield against either Manchester City or Wigan at Wembley on August 11.
Moyes said: "It's a great honour to be asked to be the next manager of Manchester United.
"I am delighted that Sir Alex saw fit to recommend me for the job. I have great respect for everything he has done for the football club.
"I know how hard it will be to follow the best manager ever, but the opportunity to manage Manchester United isn't something that comes around very often and I'm really looking forward to taking up the post next season."
Source: PA
Source: PA