The Scot was appointed as manager of the Hammers in November after the club sacked Slaven Bilic following their poor performances during the early stages of the season.
Moyes was appointed with an objective to keep the club in the Premier League and he has achieved his mandate, guiding the East Londoners to a 13th place finish in the League this season.
All in all, Moyes went on to win nine games and draw ten after managing the club 31 times in all competitions.
While the Hammers are satisfied with the job that Moyes has done, they would like to now hire a manager who can help them advance up the standings and perhaps challenge for a place in Europe next term.
Moyes was appointed on a contract which ran till the end of the season and no official announcement has been made as yet.
Some will consider this decision by the Hammers to be harsh as it can be argued that Moyes should have been given more time. However, the 55-year-old’s most recent managerial stints with the likes of Sunderland and Real Sociedad were not impressive and the Hammers hierarchy are therefore also justified if they do not see him as an ideal long-term fit.