United chief executive David Gill said the club "will move relatively quickly" in naming a successor to Ferguson, who will retire at the end of the season after 26 trophy-filled seasons at Old Trafford.
British bookmakers immediately installed Moyes as odds-on favourite to land one of the top jobs in world football, with Ferguson having previously included his fellow Scot in a short list of potential replacements.
The 50-year-old Moyes is a fiery, no-nonsense coach in the Ferguson mould and has shown loyalty and staying power in his 11 years with Everton — attributes that should go down well at United after Ferguson's reign of more than a quarter-century.
"He's cut from the same cloth," said former United defender Steve Bruce, who will manage Hull in the Premier League next season.
Real Madrid coach Jose Mourinho, Borussia Dortmund coach Juergen Klopp and Ole Gunnar Solskjaer, a former United striker who has made an impressive start to his managerial career at Norwegian side Molde, are also viewed as contenders.
Moyes, who met Everton owner Bill Kenwright for a pre-arranged meeting in London on Wednesday, has craved the chance to manage an established European side and reportedly came close to taking over at Tottenham and Chelsea in recent seasons. Many believe he has served his time at Everton — he is the third longest-serving manager in the league behind Ferguson and Arsenal manager Arsene Wenger — and deserves to finally move to a club of United's stature.
With a tight budget, Everton is likely to finish sixth in the Premier League, ahead of Merseyside rival Liverpool for the second straight season. That hasn't happened since 1937.
"What we are looking for is not someone to come in for 10 months or three years, we want someone to come stay there and give stability," former United goalkeeper Peter Schmeichel said. "When we talk about Moyes, he has been a decade at Everton and done a fantastic job on limited funds."
Gill alluded to a preference for longevity and managers "who got involved in the whole aspect of the club, whether it be from the youth team up to the first team."
"(The new manager will need) all aspects of it and that degree of loyalty and the understanding of the football club," he said. "Those are the sort of things we'll be looking at. Clearly he has to have the requisite football experience, both in terms of domestic and European experience, so I think it's a small pool but we'll move forward."
United has always appeared a natural fit for Moyes, despite critics often pointing to his record of never having beaten United, Liverpool, Arsenal or Chelsea away in the Premier League. He also has limited experience of managing world-class players and Everton has never played in the Champions League proper. The closest the team came was in 2005 when it lost to Spanish side Villarreal in the final qualifying round.
However, he would have the blessing of Ferguson, who said on Wednesday he will remain involved in the club as a director and ambassador and is sure to have a say in who succeeds him.
"Pep Guardiola, Jose Mourinho, David Moyes ... there's a lot of successful managers out there," Ferguson said at the start of this year, answering a question about a worthy successor.
Being mentioned in the same sentence as Guardiola and Mourinho can't help but boost Moyes' belief. United has never had a foreign coach, either.
Mourinho has been heavily linked with a return to Chelsea this summer, but the United job is clearly one he would relish. He has the gravitas and experience to step into Old Trafford and take over from the man he dubs "The Boss."
Mourinho has won a domestic league title at every club he has managed — Porto, Chelsea, Inter Milan and Madrid — and won the Champions League with Porto and Inter.
At the recent Champions League last-16 match between Madrid and United, Mourinho went out of his way to say all the right things in pre-and post-match news conferences, even saying the "best team lost" after Madrid sneaked through on aggregate after struggling in the second leg.
Mourinho knows the Premier League well from his three seasons at Chelsea from 2004-07. But he has yet to build an empire at any of his clubs — three years is the most he has spent at one team — and that may be looked down upon in United circles.
With Guardiola already committed to joining Bayern from next season, the candidates to replace Ferguson are few and far between.
Rafa Benitez's short-term contract is up at Chelsea at the end of the month but it would be hard to see him at Old Trafford after his run-ins with Ferguson during his time at Chelsea.
Klopp is highly rated and regularly linked with a move to the Premier League, but it may be too soon for him.