The 19-year-old, from Burntwood in Staffordshire, raised more than £3.2m for the Teenage Cancer Trust after news of his plight spread on social media.
In a post on Facebook announcing Stephen's death, Jane Sutton said he was a "courageous, selfless, inspirational son" and died peacefully in his sleep.
Stephen was diagnosed with terminal cancer aged 15.
Ms Sutton added: "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."
Stephen was readmitted to hospital on Sunday after developing breathing difficulties caused by the re-growth of tumours.
All of us at Office Green offer our sincere condolences to Stephen's family and friends.