The Prime Minister said she played a crucial role in helping peace to take root in Northern Ireland and had been a "key architect" of New Labour.
Mr Blair, who appointed her Northern Ireland Secretary after the Labour victory of 1997, said she was "great company, utterly irreverent, full of life and fun".
He added: "Behind that extraordinary front presented to the world was one of the shrewdest political minds I ever encountered. She was a natural politician, could read a situation and analyse and assess it as fast as anyone." She was a "totally modern social democrat", he said, but was equally at home with traditional trade unionists.
Mr Blair added: "It is no exaggeration to say she transformed the politics not just of Northern Ireland itself but, crucially, of relations between the Republic of Ireland and the United Kingdom, and it was this transformation that created the culture in which peace-making could flourish.
Lord Kinnock, the former Labour leader, described Ms Mowlam as "one hell of a woman". He said: "She was immensely courageous - not only personally, which she demonstrated in the months leading up to her death, but also intellectually."
He added: "Her greatest gift was her normality, the fact she could relate to people, and she made even opponents get a better understanding of the arguments they were having. That was the great armament that she had and she took to Northern Ireland."
In Northern Ireland, where Ms Mowlam oversaw the talks that resulted in the Good Friday Agreement of 1998, political leaders praised her tenacity and determination in brokering the deal.
David Trimble, the Former Ulster Unionist leader, said negotiating with her had been "like a breath of fresh air". He said: "It was clear where you were and what she wanted. And you could have a good argument with her one day and have good relations with her the next day, and that's precisely what I wanted."
Martin McGuinness, the Sinn Fein chief negotiator, whose party's car was bugged on her orders, said: "She played a crucial role in the Good Friday Agreement and it is that Agreement which will be remembered as her political legacy."
Bertie Ahern, the Irish Taoiseach, said: "If politics is about securing change for the common good, the peace and prosperity we enjoy today are a measure of how Mo's sense of public service has transformed the lives of people across these islands."
Irish President Mary McAleese said: "She brought great spirit and courage to all aspects of her life, both professional and personal and will be sadly missed by all who knew and worked with her."
Michael Howard, the Tory leader, said: "She displayed considerable bravery, both in her personal battle against serious illness and in tackling difficult political issues, often employing her engagingly unorthodox style to great effect. Her honesty and sense of fun enriched our national life.
Charles Kennedy, the Liberal Democrat leader,said: "She displayed great courage and deep humanity both in her public life in politics and privately coping with her illness."
Former Speaker of the House of Commons Baroness Boothroyd said: "Her death is heartbreaking for those of us who loved her, and it is tragic indeed that she did not live to see her passionate commitment for the peace process come to fruition."
Tony Blair, Prime Minister
"Behind that extraordinary front was one of the shrewdest political minds I ever encountered"
Neil Kinnock, former Labour leader
'She was one hell of a woman. Her greatest gift was her normality, the fact that she could relate to people'
David Trimble, former Ulster Unionist leader
'She was like a breath of fresh air. You could have a good argument with her one day and good relations the next'Reuse content