In a statement posted on the Stephen's Story Facebook page, the 19-year-old's family said he passed away peacefully in his sleep in the early hours of this morning.
Stephen, from Burntwood, Staffordshire, was readmitted to hospital on Sunday after developing breathing difficulties caused by the re-growth of tumours.
In a statement posted on Facebook, Stephen's mother, Jane, said: "My heart is bursting with pride but breaking with pain for my courageous, selfless, inspirational son.
"The ongoing support and outpouring of love for Stephen will help greatly at this difficult time, in the same way as it helped Stephen throughout his journey.
"We all know he will never be forgotten, his spirit will live on, in all that he achieved and shared with so many."
Comedian Ricky Gervais tweeted: "RIP Stephen Sutton. A true hero & inspiration to us all. #stephensstory"
TV presenter Matt Johnson tweeted: "Just read that Stephen has passed. He was, and always will be an inspiration #StephensStory @_StephensStory"