The Australian was diagnosed with testicular cancer in 2011 after a random drugs test at the U-17 World Cup had uncovered a tumour.
After undergoing surgery and chemotherapy, Tombides was able to return to action and made his first team debut for the Hammers in September 2012 during a League Cup tie against Wigan Athletic.
However, his illness then returned and Tombides passed away on Friday afternoon, surrounded by his family.
A statement on West Ham's official website read: "Dylan 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 summer 2011.
"Dylan was respected by everyone who knew him for his intelligent views on the game and his larger life 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."
"The thoughts of everyone associated with the club are with his parents Tracylee and Jim, brother Taylor, his family and friends at this sad time.
"The club request that their privacy is now respected and they are allowed to grieve their much loved son and brother in peace."
Tombides represented West Ham at youth level as well as playing for Australia at U-17 and U-22 level, and was being regarded as a very exciting talent
"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, the Football Federation of Australia's CEO, said in a statement.
"The Tombides family has lost a fine young man and Australian football has lost one of its most promising football players.
"He will be remembered for the courage he showed in his personal battle as much as the prodigious talent he displayed on the football field."
Many from the world of football have tweeted their condolences and messages of support to Tombides and his family.
All at CFC are deeply saddened at the passing of West Ham's Dylan Tombides. Thoughts with his friends, family and team-mates.— Chelsea FC (@chelseafc) April 18, 2014
Such tragic news about Dylan Tombides. Thoughts are with his loved ones RIP— Joseph Barton (@Joey7Barton) April 18, 2014
So so sorry to hear the news that Dylan tombides has passed away ! Thoughts are with his family x— Robbie Savage (@RobbieSavage8) April 18, 2014
Men, after the tragic death of Dylan Tombides from testicular cancer please please check yours for lumps. Too many dying needlessly.— Stan Collymore (@StanCollymore) April 18, 2014
Devastated to hear the news of Dylan Tombides passing. Such a brave fight of this horrible disease. Our thoughts go to his family #whufc— Brad Jones (@Brad_Jones1) April 18, 2014