The 20-year-old, who was diagnosed with the illness in 2011, passed away with his family at his side this morning.
A statement on the club's website said: "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."
The club will hold a minute's applause at Upton Park ahead of tomorrow's Premier League match against Crystal Palace.