He prompted a surge of donations to the charity last week after posting a farewell fundraising plea on the social networking site Facebook.
Sutton, who was diagnosed with bowel cancer aged 15, started raising money for the charity as part of a wish list of activities he wanted to complete before he died. His initial aim was to raise £10,000 for the organisation, but he later revised this to £1m.
He posted yesterday: "One week ago I posted a ‘thumbs up farewell’ photo that went viral," he said. "At that point I genuinely thought I was a goner, but one week on I’m still here!"
Sutton said that his condition was improving in the short term. "We can optimistically look forward to a period of ‘future’ that at the beginning of the week seemed impossible," he wrote.
His JustGiving page has received more than 128,000 donations totalling more than £3.07m.
Siobhan Dunn, chief executive of the Teenage Cancer Trust, said: "Both Stephen and the Teenage Cancer Trust are completely overwhelmed by the phenomenal public and celebrity support that Stephen’s story has gained and is still continuing to gain.
"We’re not a huge charity and normally raise only about £12m a year, so to raise to date £3m will make a massive impact on our work and enable us to support so many more young people with cancer across the UK."