Her spokesman Lord Bell confirmed that Mrs Thatcher died this morning.
She was 87.
Lord Bell said: "It is with great sadness that Mark and Carol Thatcher announced that their mother Baroness Thatcher died peacefully following a stroke this morning.
"A further statement will be made later."
In a statement on the Downing Street Twitter feed, David Cameron said: "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."
Sir Bernard Ingham, who was Baroness Thatcher's chief press secretary when she was prime minister, told the Press Association: "It's a very sad day. We have lost the outstanding peacetime prime minister of the 20th century.
"She was the perfect prime minister - she knew what she wanted to do, and did it.
"Her 11 years were quite outstanding, and raised the standing of Britain in the world, and changed the nature of Britain itself."
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? email@example.com