The Scot had guided the club to eight wins during his tenure, including success over Chelsea and a 4-1 thumping of the impressive Huddersfield, and nine draws, taking four points from games against Arsenal, Tottenham, Chelsea and Manchester United.
The club said they would seek to recruit a "high-calibre" manager within the next 10 days.
Reports this week said West Ham had held "productive" talks with Paulo Fonseca, the manager of Shakhtar Donetsk, while Sullivan remains a long-term admirer of Newcastle's Rafael Benitez.
However, despite keeping West Ham safe, Sullivan said Moyes was only regarded as a short-term fix.
Ukraine raids Kyiv office of Russian news agency
The SBU and prosecutors had uncovered the illegal activity of a Russian-controlled media chain in Ukraine. The law enforcement bodies held the investigative actions at the office of RIA News-Ukraine.
Meghan Markle's Father Will Skip the Royal Wedding, Report Says
He said he was especially upset about the photos that make him look like a heavy drinker - which he said he's not. Markle in the days before her wedding", a Kensington Palace representative said in a statement to media outlets .
Chelsea must show ambition with new signings, says Hazard
Chelsea won the Premier League in Conte's first season as head coach for Hazard's second championship winners' medal in England. And if Madrid come calling for Hazard, they would represent a tempting proposition for the 27-year-old.
Former Manchester City boss Manuel Pellegrini is one of the names in the frame for the job.
"We had to get the players in order a little bit after we came in, and we have done that", he said.
The Hammers have been in disarray this season and supporters are furious over what they feel are a string of broken promises regarding ambition, transfer spending and the much-heralded move to the London Stadium.
Gold also felt that injuries had contributed to a disappointing season for West Ham, adding: "We were disappointed at our performance right the way through the year".
West Ham's statement came just hours after Everton announced the sacking of Sam Allardyce.