The trio were informed at the London Stadium ahead of their Carabao Cup clash with Hull City, and immediately left the ground with the game going ahead.
Diop and Cullen were originally both named in the starting line-up for the clash, before being replaced ahead of kick-off.
In a statement published on the West Ham website, the club confirmed the news:
"West Ham United can confirm that David Moyes, Issa Diop and Josh Cullen have returned positive tests for COVID-19."
"The club’s medical team were informed of the test results as the team were at London Stadium preparing for this evening’s Carabao Cup third round tie against Hull City. The manager and both players immediately left the stadium and have returned home.
"All three, who are asymptomatic, will now follow Public Health England and Premier League guidelines and protocols.
"Everyone at West Ham United send their best wishes to David, Issa and Josh.
"Tuesday’s match will go ahead as planned, with Assistant Manager Alan Irvine taking charge of the team."
Wolves are due to travel to the capital this weekend ahead of the clash with the Hammers at the London Stadium.