The prime minister, who is cutting short his trip to visit European leaders, said: "It was with great sadness that I learned of Lady Thatcher's death. We've lost a great leader, a great prime minister and a great Briton."
Downing Street has said Thatcher's funeral will take the same form as that for the Queen Mother and princess Diana.
Boris Johnson said he was "very sad" to hear of death of Thatcher. "Her memory will live long after the world has forgotten the grey suits of today's politics," he said.
Former Conservative leader Michael Howard, who was employment secretary under Thatcher, sad: "She was a titan in British politics. I believe she saved our country."
Work and pensions secretary Iain Duncan Smith, another former Tory leader, said: "Baroness Thatcher was the reason I came into politics. She bestrode the political world like a colossus".
Politicians from across the political spectrum also took to Twitter today to pay tribute to the former prime minister.
Labour MPs also sought to avoid making political points as news of Thatcher's death broke. Ed Miliband said she "defined the politics of the 1980s".
"I send my deep condolences to Lady Thatcher's family, in particular Mark and Carol Thatcher," he said.
"She will be remembered as a unique figure. She reshaped the politics of a whole generation. She was Britain's first woman Prime Minister. She moved the centre ground of British politics and was a huge figure on the world stage.
"The Labour Party disagreed with much of what she did and she will always remain a controversial figure. But we can disagree and also greatly respect her political achievements and her personal strength.
"She also defined the politics of the 1980s. David Cameron, Nick Clegg and I all grew up in a politics shaped by Lady Thatcher. We took different paths but with her as the crucial figure of that era.
"She coped with her final, difficult years with dignity and courage. Critics and supporters will remember her in her prime."
Liberal Democrat leader and deputy prime minister Nick Clegg said Mrs Thatcher had been one of the "defining figures in modern British politics".
Former Labour prime minister Tony Blair said “Margaret Thatcher was a towering political figure".
"Very few leaders get to change not only the political landscape of their country but of the world. Margaret was such a leader. Her global impact was vast," he said.
"And some of the changes she made in Britain were, in certain respects at least, retained by the 1997 Labour Government, and came to be implemented by governments around the world.
"As a person she was kind and generous spirited and was always immensely supportive to me as Prime Minister although we came from opposite sides of politics."
Ukip leader Nigel Farage said he was "very sad" to hear of the death, adding that Thatcher was a "great patriotic lady".
Conservative backbenchers poured on to Twitter with tributes. Foreign Office Minister Hugo Swire: "Very sad about Margaret Thatcher but what a life. Hugely privileged to have known her."
John Whittingdale, the chairman of the culture committee who served as Thatcher's political secretary between 1988 and 1992, told BBC Radio 5 Live: "On a personal level she displayed enormous kindness, she inspired huge loyally among her personal staff," he said.
"She was a very compassionate person, at the same time she was avery strong eader she almost defined the term conviction politician."
Therese Coffey said Thatcher had "transformed" the country, "putting Great back in Great Britain".
Sarah Wollaston said: "So sad to hear of the death of Baroness Thatcher. An exceptional woman & great Briton. We should be proud of our Iron Lady."
David Burrowes said: "Very sad news of the death of Margaret Thatcher. A truly great PM, transformed Britain holding high the torch of liberty home and abroad."
Chris Heaton-Harris said: "RIP Baroness Thatcher. Few politicians get to win a battle of ideas, let alone inject hope & belief into a nation."