The former cabinet minister died at home on Saturday evening after being diagnosed with a brain tumour last year.
Former prime minister Tony Blair, in whose Cabinet Dame Tessa served as culture secretary, said she would be remembered for being "the most wise of counsellors, the most loyal and supportive of colleagues, and the best of friends".
He said: "There was no one like Tessa and no one better. I will miss her more than I can say.
"My thoughts and prayers, and those of Cherie and all the family, are with David and her wonderful family of whom she was justly very proud."
Highlighting her work in the implementation of the Sure Start programme, as well as her drive to narrow the pay gap, Mr Blair hailed her "remarkable" achievements.
She was also instrumental in London's successful bid for the 2012 Olympic Games.
Lord Sebastian Coe, former chairman of the London Organising Committee, said there would not have been a London 2012 without her.
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.
"And long after the Games were over, Tessa continued to fight for their legacy. Without her the sporting landscape of the UK would have looked very different, and so many other tangible legacies left dormant. I will miss her enormously."
Former acting Labour leader Harriet Harman said Dame Tessa was "no softie", adding: "She was clever and tough."
"Tessa was my MP neighbour for 23 years, always courteous and polite with local agencies, hospitals and schools.
"But if they were misleading, uncaring or obfuscating she would be tougher than anyone - and forensic with it.
"But above all she wanted to see Labour in government, and when we were she took her unique style and deep personal commitment into the heart of Whitehall."
John Bercow, Speaker of the House of Commons, described Dame Tessa as an "indefatigable campaigner who translated care from a word to a deed at every turn".
He added: "Through her focus on Early Years provision, Tessa did more than most to improve lives and promote social justice.
"Passionate, warm and empathetic, she saw the best in everyone and won respect and affection across the political spectrum."
Helen Hayes MP, who succeeded Dame Tessa as the MP for Dulwich and West Norwood in 2015, hailed her "extraordinary" legacy, and said she had served her constituents "with a commitment to making a difference every single day".
Councillor Georgia Gould, leader of Camden Council, said her optimism and courage were a "massive inspiration" to many.
After being diagnosed with a brain tumour in May 2017, Dame Tessa worked to raise awareness about the realities of cancer, and made an impassioned plea in Parliament for better treatments for patients.
Sarah Lindsell, chief executive of the Brain Tumour Charity, said: "Tessa Jowell's courage and honesty in speaking about her brain tumour diagnosis, coupled with her fierce determination to improve the lives of others affected by the disease, has already brought hope to an often-forgotten community of patient and families.
"As at so many times in her life, she has been an extraordinary driving force for change. Her passionate support for more flexible clinical trials for brain tumour patients, and for global data-sharing to improve understanding of the disease, will have a real and lasting impact in our quest for a cure."