The club confirmed the news on Monday evening, amid reports former Spain, Real Madrid and Wolves boss Julen Lopetegui had agreed a deal to take over in the summer.
The Spaniard guided Wolves to safety last term, but left on the eve of the new Premier League campaign in August. The 57-year-old had lifted Wolves from the bottom of the table to a 13th-placed finish during his nine-month spell in charge.
Moyes, 61, was in his second spell at West Ham after a six-month period in 2017-18 when he lifted them out of the relegation zone. He returned in December 2019 with the club struggling again.
Moyes said: "I have enjoyed four and a half brilliant years at West Ham, and the club is in a stronger position than when I returned back in 2019.
"When I joined West Ham for a second time, the club was one place above the relegation zone, and it has been a terrific journey to have achieved three consecutive seasons in Europe.
"After leading the club to safety, we guided the team to finishes of sixth and seventh in the Premier League, and I was delighted when we won the Europa Conference League title last June - the club's first major trophy in 43 years.
The Hammers said the recruitment process for Moyes' successor had begun and they would make no further comment on the matter until the new appointment was confirmed.
After a modest playing career Moyes made his name as a manager at Preston North End then enjoyed a successful 11 years at Everton before becoming Alex Ferguson's successor at Manchester United.
That proved short-lived and the Scot subsequently managed Real Sociedad and Sunderland before West Ham.
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