Dame Tessa died on Saturday after her selfless battle with brain cancer, her family announced on Sunday Morning.
'My thoughts and prayers are with her family at this hard time'.
Dame Tessa recently spoke movingly in the House of Lords about her condition and called for patients to have better access to experimental treatment.
Then-Prime Minister Tony Blair asked Ms. Jowell to coordinate the government's support for survivors and the bereaved.
The leader of the Labour party Jeemy Corbyn said her fight to raise awareness of cancer "inspired us all".
Mrs May wrote: "The dignity and courage with which Dame Tessa Jowell confronted her illness was humbling and it was inspirational.
My sympathies to her loving family - Dame Tessa's campaigning on brain cancer research is a lasting tribute to a lifetime of public service".
This caller told Maajid how Dame Tessa Jowell was Tony Blair's "greatest gift" to the 7/7 community, after her daughter was killed in the attacks on London in 2005.
When Gordon Brown took over, she was demoted from her cabinet role but retained her Olympics portfolio.
Figures from the world of sport praised her involvement as culture secretary in bringing the Olympic Games to London. "I will miss her enormously".
"I saw the forward-looking, expansive, optimistic vision of Britain that the opening ceremony represented and I thought again that this was something the bombers and their supporters would have hated - all those nations, with their different views, their different cultures, their different traditions, coming together in a spirit of peace and play", she said.
Dame Tessa will be remembered at Westminster as someone who managed to be ideologically committed to her cause without overt sectarian bitterness.
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 fearless fight".
"London 2012 simply wouldn't have happened without her. My heartfelt condolences to her family & friends".
"She had said at the time that In the end, what gives a life meaning is not only how it is lived, but how it draws to a close", she said in the speech.
So there we are - me and the former Olympics Minister - going in circles at 6am in an empty park as I tried desperately to remember the way.
She was pro-European and in favour of a mixed-economy when both were deeply unfashionable on the left.
"But if they were misleading, uncaring or obfuscating she would be tougher than anyone - and forensic with it".
Dame Tessa was appointed Deputy Mayor of the Olympic Village in recognition for her efforts in getting London the Games.
She also remained on the 2012 Olympics Organising Committee under chairman Sebastian Coe.
"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. "Without her the sporting landscape of the United Kingdom would have looked very different", said Lord Coe.
Her successor in Dulwich, Helen Hayes MP, tweeted: "So very sad at the passing of my friend & predecessor Tessa Jowell who served Dulwich & West Norwood for 23 years".
"Her accomplishments are enormous but just as impressive is how she achieved them: with decency, determination, guts and grace".