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"The club would like to place on record its thanks for the hard work, honesty and integrity he brought to the role," the club said in a brief statement.
Moyes was told he would "leave the club" by executive vice chairman Ed Woodward in an 8am meeting at United's Carrington training base on Tuesday morning.
It brings an ignominious end to an apocalyptic campaign for the Scot, who oversaw United's ejections from the FA Cup and League Cup in January, as well as an unprecedented 11 Barclays Premier League defeats.
On Sunday, Moyes' former club Everton comfortably defeated United 2-0 to end any lingering hopes of Champions League qualification, bringing United's 18-year stint in the competition to an end.
Moyes managed United for the final time against his former club at Goodison Park
That Moyes' final match in charge of United came at Everton is as galling for him as it is satisfying for Evertonians. Everton will finish above United for the first time since 1990, which is just one of several excuses United had to dismiss Moyes.
Selected personally by Ferguson to replace him, Moyes has broken several unwanted records despite inheriting a title-winning squad and spending £64.6 million on Marouane Fellaini and Juan Mata.
Moyes was confirmed as Ferguson's successor on 9 May, just a day after his predecessor announced his retirement, having managed Everton for 11 years.
Despite having the best part of two months to prepare for his debut campaign at Old Trafford, Moyes only made one signing in the summer transfer window - Fellaini - on deadline day, which was the precursor to a disastrously brief tenure at United.
His appointment reflects horrendously on Ferguson and Sir Bobby Charlton, who chose the former Everton manager over José Mourinho last year. Mourinho, who was so intent on replacing Ferguson at United he reportedly cried when he discovered the club had chosen Moyes, instead returned to Chelsea.
Moyes' reign was undermined by comments from a number of players. Rio Ferdinand opined Moyes' selection policy was "driving him mad", Anderson, farmed out on loan to Fiorentina, claimed a number of United players "want out" and, following the Olympiakos humiliation, Robin van Persie questioned Moyes' tactics.
Van Persie, and a number of other players, were unhappy with the training under Moyes, specifically the lack of time spent on final-third finishing.