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."
Stephen, who was diagnosed with metastatic bowel cancer aged 15, was visited earlier this month at Birmingham's Queen Elizabeth Hospital by Prime Minister David Cameron, who praised his "incredible" efforts to help others.
In a statement after news of Stephen's death was announced, the Teenage Cancer Trust said: "We are humbled and hugely grateful for what Stephen achieved and continues to achieve for us.
"The thoughts of everyone here at Teenage Cancer Trust are with Stephen's family and friends."
Donations to the Trust via Stephen's fund-raising page - www.justgiving.com/stephen-sutton-tct - continued to pour in as news of his death spread on social media.
One person making a donation to Stephen's JustGiving appeal wrote: "What a fantastic, eloquent, inspirational young man.
"May you rest in peace. Thank you for sharing your life with us. Truly sad today."
In a message posted on his Twitter page, Mr Cameron said: "I'm deeply saddened to hear that Stephen Sutton has died. His spirit, bravery and fundraising for cancer research were all an inspiration."
Comedian Jason Manford, who helped to champion Stephen's fundraising, said today: "Stephen Sutton was the most inspiring person I've ever met and touched more lives than he will ever know.
"He was an incredibly positive young man and a credit to his family, to Burntwood and to humanity itself. The reason we took to him so passionately was because he was better than us, he did something that none of us could even imagine doing.
"In his darkest hour he selflessly dedicated his final moments to raising millions of pounds for teenagers with cancer.
"Some of Stephen's words will stay with me and others forever and they are words to live by - 'life isn't measured in time, it's measured in achievements'. If that's true, Stephen, then you had a fulfilling life full of special moments and you will live long in the memory of thousands, if not millions, of people."
Siobhan Dunn, chief executive of Teenage Cancer Trust, said: "Stephen was an exceptional young man and ambassador for Teenage Cancer Trust. He will be remembered for his incredible positivity by all who met or connected with him.
"Stephen didn't measure life in time, preferring instead to measure it by the difference someone makes. Stephen has made an enormous difference to Teenage Cancer Trust and the seven young people diagnosed with cancer every day who need our help."
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"