London's successful bid to host the 2012 Olympics would become one of Dame Tessa's most notable achievements.
Her last few months saw her campaign for more cancer treatments to be made available through the NHS.
"Tessa was a true believer in the power and inspiration of sport, for which all of us who benefited from her support and conviction will be eternally grateful", said Grainger, who won rowing gold for Great Britain at London 2012.
He said: 'Tessa Jowell was an inspirational woman and committed parliamentarian.
Dame Tessa gave a moving speech in the House of Lords in January, in which she expressed her hope that "we can live well with cancer, not just die of it".
In a statement released today, her family said: "Tessa, who was 70, was diagnosed with a gliobastoma multiforme brain tumour in May a year ago, suffered a haemorrhage on Friday, and had been in a coma since then. She was the most wise of counsellors, the most loyal and supportive of colleagues, and the best of friends". "She will be remembered for many things including of course successfully bringing us the London Olympics". "I will miss her enormously".
Lord Sebastian Coe, president of the IAAF and former chairman of the London organising committee of the Olympics, said: "Tessa was not just a close friend, she was a life enhancer".
David Cameron shared a picture of himself and Dame Tessa recreating the Beatles' Abbey Road cover, writing: "Devastated that Tessa Jowell has passed away after her incredibly courageous fight. My heartfelt condolences to her family & friends". "Deepest condolences to her family".
"But if they were misleading, uncaring or obfuscating she would be tougher than anyone - and forensic with it".More news: Everton star wants Rooney to stay at Goodison Park
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Cllr Peter John tweeted: "Following the sad death of Dame Tessa Jowell, who served as constituency MP for Dulwich & West Norwood between 1992 and 2015, Lambeth and Southwark Councils are opening books of condolence at their respective Town Halls".
Here she took on the job of convincing unsure colleagues about the merits of hosting the Olympics in 2012.
He said: "No politician deserves greater credit for the Games".
"She showed unflinching tenacity in persuading the prime minister and the cabinet that the government should throw its full weight behind the bid", he said.
"And long after the Games were over, Tessa continued to fight for their legacy".
Though losing her Cabinet post in Gordon Brown's 2007 reshuffle she remained Olympic minister and oversaw every stage of the games from initial bid to competition. Without her the sporting landscape of the United Kingdom would have looked very different, and so many other tangible legacies left dormant.
Labour MPs and others recognised her warm personality, strong sense of compassion and dry sense of humour.
He added: "Through her focus on Early Years provision, Tessa did more than most to improve lives and promote social justice".