The Scot has guided the Hammers into the Europa Conference League final despite a poor domestic campaign.
The Irons ended their own 47-year wait for a European final after beating Dutch side AZ Alkmaar 3-1 on aggregate.
But the club finished a lowly 14th, only six points above the relegation zone, in the Premier League this season.
West Ham's flirtation with the drop at times this season was a huge shock after heavy summer investment in Gianluca Scamacca and Lucas Paqueta.
And speculation surrounding Moyes' future has been rife for much of 2023.
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Could Moyes leave West Ham this summer?
talkSPORT's chief football correspondent Alex Crook revealed in March that Moyes is fighting to save his job beyond this season.
Having survived the international break, West Ham owner David Sullivan was reluctant to make a change before the summer.
Sullivan was steadfast in his belief that Moyes was still the best man to deliver safety and the Scot fulfilled on that promise.
However, talkSPORT confirmed that it is increasingly likely Moyes will not see out his contract, which expires in the summer of 2024.
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Ange Postecoglou is closing in on being appointed as the new Tottenham manager with Moyes linked with replacing him at Celtic.
"I've never even considered it," Moyes said in his pre-match press conference.
"I'm the West Ham manager and I'm really enjoying my period here and the club have been so good to me.
"We've enjoyed the journey we're on here. I'm hopefully trying to continue growing a really good football club and I've not really taken any consideration (about the new Celtic links).
"Through the years I've been linked with lots of different jobs at different times through my career.
"But I've got to say I'm really happy at the moment and settled where I am."