The Hammers announced the decision on their official website on Wednesday:
"I would like to place on record my sincere thanks to David Moyes and his staff for achieving the target of keeping West Ham United in the Premier League," said co-chairman David Sullivan. "Throughout his time here, David has carried himself with dignity and honesty and we have all found him to be a pleasure to work with."
Moyes was appointed by West Ham in November on a short-term deal after the departure of Slaven Bilic.
When the Scotsman took over, the club were down in 18th position in the Premier League table, and despite some wobbles late in the campaign, he eventually steered them to 13th position.
Despite that, the club have decided the 55-year-old is not the man to take them forward. Per Jacob Steinberg of the Guardian, the club have already held discussions with Shakhtar Donetsk manager Paulo Fonseca about taking over the position.
As noted by Steinberg, the message coming out of the club from those in positions of power is confusing at the moment:
Moyes arrived at West Ham with his reputation in tatters, as he was in charge as Sunderland dropped into the Championship after a miserable 2016-17.
Prior to that, he had endured torrid spells with both Manchester United and Real Sociedad. Moyes had previously established himself as a fine coach during an 11-year stint with Everton, during which time he made the Toffees into regular challengers for European places.
At West Ham, Moyes did settle the team down and was able to rejuvenate some players who had been underperforming. The most notable improvement came in the game of Marko Arnautovic, who has been converted into a centre-forward and been exceptional.
Jonathan Northcroft of the Sunday Times pointed to some of the other positive moves Moyes made during his brief time at the club:
Jonathan Northcroft @JNorthcroft
Moyes: Arrived with WHUFC 18th Finished 13th Got Arnautovic playing Found Masuaku's position Had Reid, Obiang, Carroll, Lanzini, Antonio injured Cleaned up culture/discipline Restored work ethic As owners hid, dealt with their crises Nae cash Good luck to the next guy...
Nevertheless, West Ham clearly have big ambitions, and to fill the London Stadium every week, an exciting side is needed. Moyes is not the manager who will bring gripping football to east London.
The potential is there for the Hammers to do well with the right manager, as there are talented players in the squad and a fanbase backing them desperate for success. However, in recent years, the higher-ups at the club have made a string of bad decisions; it's imperative they get this one right when appointing Moyes' successor.