As tributes poured in to the former premier, it was announced that she will receive a ceremonial funeral with military honours at St Paul's Cathedral.
Downing Street gave details of the event after the Tory former prime minister died this morning. She had been in ill health for several years and was rarely seen in public in recent years.
The Queen was said to be "sad" at news of her death and Prime Minister David Cameron praised her as a "great leader" and a "great Briton".
Liberal Democrat leader Nick Clegg said Mrs Thatcher had been one of the "defining figures in modern British politics".
A Number 10 spokesman said: "We can announce that, with the Queen's consent, Lady Thatcher will receive a ceremonial funeral with military honours.
"The service will be held at St Paul's Cathedral. A wide and diverse range of people and groups with connections to Lady Thatcher will be invited.
"The service will be followed by a private cremation.
"All the arrangements being put in place are in line with wishes of Lady Thatcher's family. Further details will be published over the coming days."
Mr Cameron is returning early from an official trip to Spain after the news of Baroness Thatcher's death was announced by her spokesman, Lord Bell. She is understood to have been recuperating at the Ritz Hotel in London after a minor operation.
Baroness Thatcher earned a place in the history books as the first woman prime minister when she entered Downing Street in 1979.
Over the next 11 years even her critics admitted that she changed the face of the country.
"It was with great sadness that l learned of Lady Thatcher’s death. We've lost a great leader, a great Prime Minister and a great Briton"— UK Prime Minister (@Number10gov) April 8, 2013
In recent years her health deteriorated, and she stopped making public appearances.
Lady Thatcher suffered several small strokes in 2002, and received medical advice against accepting any more public speaking engagements.
Her increasingly frail condition when she was seen - especially after the death of husband Denis in 2003 - led to frequent bouts of speculation about her health.
However, MPs and friends who saw her regularly said she remained alert and interested in politics, and she was not known to have deteriorated notably recently.
There have been calls for the ex-premier to receive a state funeral, although she was a divisive figure for many on the Left.
Labour leader Ed Miliband said: "I send my deep condolences to Lady Thatcher's family, in particular Mark and Carol Thatcher.
"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."
Former 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. 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.
"Even if you disagreed with her as I did on certain issues and occasionally strongly, you could not disrespect her character or her contribution to Britain's national life. She will be sadly missed."
Prime Minister David Cameron told the BBC: "Today is a truly sad day for our country. We've lost a great prime minister, a great leader, a great Briton.
"As our first woman prime minister, Margaret Thatcher succeeded against all the odds, and the real thing about Margaret Thatcher is that she didn't just lead our country, she saved our country, and I believe she'll go down as the greatest British peacetime prime minister.
"Today is obviously a day we should most of all think of her family. We've lost someone great in public life but they've lost a much-loved mother and grandmother and we should think of them today.
"Her legacy will be the fact she served her country so well, she saved our country and that she showed immense courage in doing so.
"And people will be learning about what she did and her achievements in decades, probably centuries to come.
"That's her legacy but today we must also think of her family."