Successor David Cameron called her a “great Briton” and the Queen spoke of her sadness at the death.
Lady Thatcher was Conservative prime minister from 1979 to 1990. She was the first woman to hold the role.
She will not have a state funeral but will be accorded the same status as Princess Diana and the Queen Mother.
The ceremony, with full military honours, will take place at London’s St. Paul’s Cathedral.
The union jack above Number 10 Downing Street has been lowered to half-mast.
Cameron, who was in Madrid for meetings, cancelled planned talks in Paris with French President Francois Hollande and returned to the UK late today.
Lady Thatcher’s government privatised several state-owned industries. She was also in power when the UK went to war with Argentina over the Falkland Islands in 1982.
Cameron told the BBC: “Margaret Thatcher succeeded against all the odds. The real thing is she didn’t just lead our country; she saved our country.
“I believe she will go down as the greatest British peacetime prime minister.”
A Buckingham Palace spokesman 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.”
Lady Thatcher, born Margaret Roberts, served as MP for Finchley, north London, from 1959 to 1992.
Having been education secretary, she successfully challenged former prime minister Edward Heath for her party’s leadership in 1975 and won general elections in 1979, 1983 and 1987.
Sir John Major, who replaced Lady Thatcher was prime minister in 1990, called her a “true force of nature”.
He added: “Her reforms of the economy, trades union law, and her recovery of the Falkland Islands elevated her above normal politics, and may not have been achieved under any other leader.
“Her outstanding characteristics will always be remembered by those who worked closely with her: courage and determination in politics, and humanity and generosity of spirit in private.”
Labour leader Ed Miliband said Lady Thatcher had been a “unique figure” who “reshaped the politics of a whole generation”.
He added: “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.”
Deputy Prime Minister Nick Clegg described Lady Thatcher as one of the “defining figures in modern British politics”, adding: “She may have divided opinion during her time in politics but everyone will be united today in acknowledging the strength of her personality and the radicalism of her politics.”
London Mayor Boris Johnson tweeted: “Very sad to hear of death of Baroness Thatcher. Her memory will live long after the world has forgotten the grey suits of today’s politics.”
UK Independence Party leader Nigel Farage called Lady Thatcher a “great inspiration”, adding: “Whether you loved her or hated her nobody could deny that she was a great patriot, who believed passionately in this country and her people. A towering figure in recent British and political history has passed from the stage. Our thoughts and prayers are with her family.”
Lady Thatcher had suffered poor health for several years. Her husband Denis died in 2003. (BBC)