Mrs Tomlinson, a terminal cancer sufferer, died aged 43 after a seven-year battle with the disease.
The married mother-of-three from Leeds had raised £1.75m in a series of gruelling challenges and wrote a biography with her husband Mike.
"I was greatly saddened to hear that Jane had passed away and my thoughts are with Mike and her family," said Radcliffe.
"She fought so bravely and so strongly and through her inspirational exploits raised huge amounts to help others fight this terrible disease. She will be greatly missed."
After being told in 2000 that her breast cancer was incurable, Mrs Tomlinson dedicated her life to raising money for charity and completed a string of events, including the Great North Run, London Marathon and the Ironman UK Triathlon.
She was made a CBE earlier this year, one of several honours for her fundraising work.
The story of Mrs Tomlinson first became widely known after she was honoured by the BBC before millions of television viewers in 2002.
Radcliffe presented her with the Helen Rollason Award, in memory of the former TV sports presenter who died of cancer, and given for courage in the face of adversity.
At the same event, Radcliffe was voted Sports Personality of the Year after winning the 5,000m at the Commonwealth Games in Manchester.
But she insisted Mrs Tomlinson was "a more deserving winner" than anyone else at the awards show.
