The 20-year-old Australian, who made his first-team debut in a League Cup match against Wigan Athletic in 2012, was diagnosed with the illness in 2011.
"Dylan was respected by everyone who knew him for his intelligent views on the game and his larger than life character," the club said in a statement on their website (www.whufc.com).
Tombides, who joined West Ham as a 15-year-old after a spell in Hong Kong, played for Australia at Under-17 and Under-23 level.
"On behalf of the Australian Football Community, we offer our deepest condolences to Dylan's family, team mates and friends during this extremely sad time," David Gallop, Football Federation Australia CEO, said in a statement.
West Ham will hold a minute's applause in honour of Tombides before Saturday's Premier League game against Crystal Palace at Upton Park.
(Reporting by Michael Hann, editing by Ed Osmond)
