"It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke this morning," Lord Tim Bell said, referring to Thatcher's children.
Britain's Queen Elizabeth II was saddened to hear of her death, Buckingham Palace said.
"The Queen was sad to hear the news of the death of Baroness Thatcher. Her Majesty will be sending a private message of sympathy to the family," it said.
The former premier, who led Britain from 1979 to 1990, suffered from dementia and has appeared rarely in public in recent years.
She was last in hospital in December for a minor operation to remove a growth from her bladder.
The former Conservative Party leader remains the only female premier in British history and was the 20th century's longest continuous occupant of Downing Street.
Her daughter once revealed that the former premier had to be repeatedly reminded that her husband Denis had died in 2003.
She was told by doctors to quit public speaking a decade ago after a series of minor strokes.
Michael Howard, Conservative leader 2003-2005, told Sky News television: "It's terribly sad news. She was a titan in British politics.
"I believe she saved the country, she transformed our economy and I believe she will go down in history as one of our very greatest prime ministers."
Right-wingers hailed her as having hauled Britain out of the economic doldrums but the left accused her of dismantling traditional industry, claiming her reforms helped unpick the fabric of society.
On the world stage, she built a close "special relationship" with US president Ronald Reagan which helped bring the curtain down on Soviet Communism. She also fiercely opposed closer ties with Europe.
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there is no way of passing the death..............once known as Iron Lady!
she was the architect of first iraqi invasion by allied forces under bush senior which triggered the present state of terrorism.... such personalities should be dumped into the dustbin of history... they dont deserve any respect.
Remarkable woman by any standards - respected by both the American's and Soviets. She restored a sense of national pride and purpose. Pakistan would do well to find someone with her talents/character/backbone.