Lady Thatcher's children Mark and Carol said their mother, who suffered bouts of ill health in recent years, died peacefully after suffering a stroke at the age of 87.
She died about 11am at the Ritz in central London, where she had been staying since January following a minor operation. A private ambulance drove her body from the hotel shortly before midnight.
Prime Minister David Cameron announced that Parliament would be recalled on Wednesday "for a special session in which tributes will be paid".
Downing Street, which joined Buckingham Palace and the Houses of Parliament in flying its flags at half mast, also said the politician would be given a full ceremonial funeral with honours - the same status accorded to the Queen Mother.
The Government said the memorial, at St Paul's Cathedral, is expected to take place next week and would be televised.
Members of the armed services will line the route of Lady Thatcher's funeral procession from the Palace of Westminster to St Paul's.
Her friend and spokesman Lord Bell said she did not want a state funeral and thought a fly-past over the service would be a "waste of money".
Mr Cameron today led tributes from around the world, calling the former Tory leader "a great prime minister, a great leader, a great Briton" as while mourners left flowers outside Lady Thatcher's house in Belgravia, London.
The Prime Minister said: "Margaret Thatcher didn't just lead our country - she saved our country.
"Margaret Thatcher took a country that was on its knees and made Britain stand tall again."
He added: "We can't deny that Lady Thatcher divided opinion. For many of us, she was and is an inspiration. 
"For others she was a force to be defined against. But if there is one thing that cuts through all of this - one thing that runs through everything she did - it was her lion-hearted love for this country."
Mr Cameron was in Spain at the start of a European tour to push for a more flexible EU when the news broke but immediately cut short his trip. 
Buckingham Palace added: "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."
US President Barack Obama said that America would "never forget her standing shoulder to shoulder with President Reagan" and that she had "with moral conviction" helped to shape history. 
Former Labour prime minister Tony Blair called the ex-PM a "towering political figure" who exercised a huge influence over Britain and the world.
"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," he said.
"She will be sadly missed."
The moniker stuck and privately she was thought to enjoy it. It also became the title of the 2011 biopic for which Meryl Streep won an Oscar.
Lady Thatcher was also memorably described by the then French president Francois Mitterrand with the back-handed compliment that she had the "eyes of Caligula and the mouth of Marilyn Monroe". 
But perhaps the defining moment of her career will be the decision to send a taskforce to the Falklands on April 2, 1982 after Argentina invaded.
In Stanley, Falkland Islands, in 1983
Despite her toughness, few will forget the pictures of Lady Thatcher leaving Downing Street for the last time with her husband, Sir Denis - tears in her eyes.
A woman who believed in hard work, she was the daughter of grocer Alfred Roberts and gained a degree in Chemistry at Oxford University, where she became president of the university's Conservative Association.
Her first job was as a research chemist but in February 1951 she was adopted as Conservative candidate for Dartford and at a dinner that day she met the wealthy and divorced businessman, Denis Thatcher. They married later that year.
With son Mark (L) and daughter Carol (R) at her husband's funeral in 2003
He supported her during her unsuccessful campaigns for the seat and during her studies to become a barrister. She qualified in 1953, the same year she gave birth to twins Mark and Carol.
Lord Bell said Mark is currently in Barbados, while Carol is in Switzerland. Both will be back in Britain for their mother's funeral.
Lady Thatcher had been staying at the Ritz at the invitation of its owners, David and Frederick Barclay, as her Belgravia home was not properly equipped for her recovery from illness.
