The club's new owners, the Friedkin Group, have targeted Moyes since they abruptly parted company with Sean Dyche just hours before Thursday night's FA Cup third-round win over Peterborough.
And they appear to have wasted no time in concluding a deal which will see Moyes usher in a new era for the club when they kick off at their new Bramley Moore Dock Stadium next season.
Moyes, who has been out of work since leaving West Ham at the end of last season, is reported to have agreed a two-and-a-half year deal and will be in charge against Aston Villa in the Premier League on Wednesday.
The PA news agency has contacted Everton for comment.
Dyche's reign had been effectively over since Everton's defeat at Bournemouth on January 4, with the new owners initially sounding out former Chelsea boss Graham Potter, who subsequently joined West Ham.
PA understands the surprising timing of the announcement of Dyche's departure, which came after he had held his press conference for the Peterborough game, was due to wrangling over the terms of his pay-off.
Former Everton defender Leighton Baines, now the U18s head coach, and club captain Seamus Coleman, who is currently injured, took charge against Posh.
Everton defender Michael Keane conceded the players had to take some responsibility for Dyche's sacking.
"Any time you lose a manager it's really disappointing and sad," said Keane.
"He has been brilliant for me. He's been a brilliant manager, is a brilliant manager. It's just one of those things. It's football and it doesn't always work out."
33°C