A Toffees deal was ‘done’ in December 2019, according to the Scot.
Moyes said: “When I was being offered the West Ham job, I had actually been in Germany with Farhad Moshiri to take the Everton job.
“The phone rang and it was David Sullivan — in the middle of the meeting with Everton. I had to say, ‘I can’t speak just now’.
“But Carlo Ancelotti was sacked by Napoli that night and they changed tack, even though I was due to sign the day before — I had told David.
“But the next day Everton didn’t make more contact so I phoned David and said, ‘If it’s still there . . . ’.
“And it couldn’t have gone better — it was the right choice.”
Last season Moyes guided the Hammers to their first trophy since 1965.
Jarrod Bowen pounced in the 90th minute to sink Fiorentina 1-0 in the Europa Conference League final in Prague.
And West Have have continued their revival this term.
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Only Manchester City’s 3-1 comeback victory at London Stadium ended the Hammers’ unbeaten start to the Prem campaign.
James Ward-Prowse’s diving header was overturned by the champions’ triple strike after the break.
Jeremy Doku, Bernardo Silva and Erling Haaland gave Pep Guardiola’s 2022-23 Treble winners their fifth win in five Prem matches this season.