The 38-year-old has not featured for the newly crowned champions since January, when he was sidelined with injury.
Moyes said he had not expected to be leaving Everton after 11 years in charge and had already begin planning for next season when the Old Trafford giants came calling this week.
The 71-year-old Alex Ferguson is yet to explain why he is retiring.
David Moyes will not answer questions about his new appointment at Manchester United when he speaks to journalists on Friday.
From Manchester United to Real Madrid and Chelsea to Paris St Germain, the biggest managerial overhaul is looming this summer.
Moyes also paid a rich tribute to his present club Everton, whom he will be leaving at the end of the season.
There couldn't have been a better moment than now for the 71-year-old grandfather to step away, having restored the Red Devils' dominance and Ferguson retired with an unmatched legacy.
The former Everton boss was on Thursday confirmed as the club's new manager succeeding Alex Ferguson who is retiring this month after more than 26 years at United.
David Moyes has been appointed as manager of Manchester United on a six-year contract.
Moyes, who has been at Everton since 2002, is favourite to become United's new manager following Ferguson's decision to retire at the end of the season.
Fuelling speculations that he has handed a transfer request, Rooney has changed his Twitter credentials to '@NikeUK athlete'.