Moyes took charge of Everton on over 500 occasions with the club qualifying for Europe four times during his time as manager.
His final two games as Everton manager will be against West Ham United and Chelsea.
"Everton officials will start the search for a replacement manager immediately," added the Everton statement.
Everton's Belgian international Marouane Fellaini ?tweeted: "Many Thanks Coach."
Moyes will now be in charge of a club that under Ferguson twice won Europe's top competition and lifted the English championship 13 times following the 71-year-old's arrival in 1986.
United is one of the world's biggest sporting brands, worth a reported $3.17 billion, with a fan base of more than 650 million worldwide.
Moyes arrives with United having sealed a series of lucrative sponsorship deals aimed at maximizing off-pitch revenue in order to be competitive under European football's financial fair play rules.
The club has been repaying large amounts of debt since it was bought by the American Glazer family in a highly leveraged £800 million ($1.25 billion) takeover in 2005.
This month United reported record third-quarter earnings of £91.7 million ($142 million) but an 18% increase in operating expenses plus payments on a gross debt that has fallen to £367.6 million ($572 million) meant a pre-tax loss of £3.15 million ($4.9 million) for the period.
Whether Moyes will be given significant funds to strengthen the squad for United's EPL title defense remains to be seen -- Borussia Dortmund's top scorer Robert Lewandowski has long been linked with a move to Old Trafford, but the Poland striker would command a hefty fee and wage packet.
United did not have to pay Everton compensation for Moyes, as his contract had been due to expire in July.
Moyes may need to find a replacement for Wayne Rooney, who has told the club he wants to leave according to British reports Thursday -- but United said he is not for sale.
Moyes gave Rooney his debut as a 16-year-old at Everton but they fell out when the England striker left for Old Trafford in 2004. Moyes later sued the player and his publisher over remarks made in his autobiography, but they settled out of court.
Rooney handed in a transfer request in late 2010, but was persuaded to stay by Ferguson and rewarded with a lucrative new contract that still has two years to run.