Dame Tessa, who played a major role in securing the 2012 London Olympics, was diagnosed with brain cancer in May a year ago and died on Saturday.
She had been in a coma since Friday, after suffering a haemorrhage.
Dame Tessa was regarded as having played a pivotal role in securing the 2012 Olympics for London when she served as culture secretary, before taking on the role of Minister for the Olympics and Minister for London.
In her final months, she had campaigned for better access to new treatments to all cancer patients and received a standing ovation after addressing the House of Lords in January.
Former Prime Minister Tony Blair led the tributes to Jowell, saying she had "passion, determination and simple human decency in greater measure than any person I have ever known".
The family's statement revealed that Dame Tessa died peacefully at home near Shipston-on-Stour in Warwickshire shortly after 10pm. A statement said: "In addition to chemotherapy and radiotherapy, in recent months doctors tried innovative new treatments which Tessa gladly embraced, but sadly the tumour recently progressed very quickly".
Former prime minister Gordon Brown said Dame Tessa would be remembered for her "courage, strength and compassion for others".
The former social worker lost to her Conservative rival, and was defeated again in the following year's general election. It increased university student fees and she was trying, unsuccessfully I hasten to add, to try to get me to support an increase in the fees.
"If anyone wants to know what politics can achieve they can just look at her life and how she lived it, and how she ended it as a testimony to all that's best in politics". She was the first senior politician fully to understand the importance of public health and to shift health policy towards prevention of illness and not only cure.
It was as Tony Blair's Labour culture secretary in the early noughties that she championed the capital's eventually successful bid to host the games, in the face of Civil Service and Cabinet scepticism.
"Her contribution to the Olympic and Paralympic Games is easily defined - quite simply, without Tessa there would have been no London 2012, and without Tessa they would not have been the success they were".
Prime Minister Theresa May described Dame Tessa as "inspirational".
Dame Tessa was appointed Deputy Mayor of the Olympic Village in recognition for her efforts in getting London the Games. They were the complete core of her life and I'm honored to be part of it. Thank you for giving me Matt, Tessa, and for teaching us all so much about love, kindness, optimism and courage.
"Her death leaves us with a massive loss and so many of us will miss her enormously".
" Although she was a London-centric MP, Tessa always took the trouble to talk to all her Labour MP colleagues to find out what was going on outside London".