Moyes has the backing of Sir Alex Ferguson, who confirmed his retirement yesterday, and his first official game will be the Community Shield against either Manchester City or Wigan at Wembley on Aug 11.
David Moyes said: "I am delighted that Sir Alex saw fit to recommend me for the job. I have great respect for everything he has done and 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."
Sir Alex Ferguson says: "We unanimously agreed on David Moyes. David is a man of great integrity with a strong work ethic."
With Moyes committed to concluding the season at Everton, he will not be introduced as United manager until after the campaign is over.
"I have had a terrific job at Everton, with a tremendous chairman and board of directors and a great set of players," he added.
"Between now and the end of the season, I will do everything in my power to make sure we finish as high as possible in the table.
Everton's fantastic fans have played a big part in making my years at Goodison so enjoyable and I thank them wholeheartedly for the support they have given me and the players"
"Everton will be close to me for the rest of my life."
Having decided to end his near 27-year stint at United this summer, Ferguson quickly came to the conclusion his fellow countryman would be the right man to follow.
For the Red Devils hierarchy clearly view the appointment as more than that of just a manager, and see Moyes as someone who will embed himself in the traditions of the club.
'His hard working style and steely determination and are characteristics we value at the club',said, Man Utd co-owner Joel Glazer on Moyes
David Moyes has been at Everton since 2002 and will take over from Ferguson on July 1.