The Australia youth international, who represented his country at the U17 World Cup in Mexico in 2010, was diagnosed with testicular cancer in 2011.
Tombides, who joined West Ham at the age of 15, had turned out for West Ham's U18 and U21 sides and made his senior debut for the club in the League Cup tie against Wigan in 2012.
The youngster worked tirelessly to promote awareness of male cancer, supporting the One for the Boys campaign along with celebrities including Hollywood actor Samuel L Jackson, snooker player Jimmy White and Australian singer Peter Andre.
A West Ham club statement read: "Dylan has passed away on Friday morning with his family by his side having courageously fought the disease for three years after initially being diagnosed with testicular cancer in the summer of 2011.
"Dylan was respected by everyone who knew him for his intelligent views on the game and his larger than life character.
"He was a loving son, amazing brother and well-respected member of the West Ham squad. He will be hugely missed by everyone who had the honour of knowing him."
West Ham have confirmed there will be a minute's applause in Dylan's memory ahead of their match with Crystal Palace on Saturday and the players will also wear black armbands in his honour.