She was the first woman to hold the post from 1979 to 1990. In her long political career, Thatcher's personality and style earned her the nickname of Iron Lady.
She exploded onto the political scene at the age of 34 and became the youngest woman ever elected to parliament.
"We have lost a great leader, a great prime minister and a great Briton," current Prime Minister David Cameron said in a statement.
Flags were flown at half-staff at Buckingham Palace, Parliament and Downing Street on Monday. Queen Elizabeth II authorized Thatcher to have a ceremonial funeral - a step short of a state funeral - to be held at St. Paul's Cathedral in London with military honors.
Henry Kissinger, former U.S secretary of state, called Thatcher a tremendous prime minister.
"She was a great lady. She had very strong opinions and for those of us who knew her over the decades, she was a very warm person, which is not the public image that is often given," said Kissinger.
For admirers, Thatcher was a savior who rescued Britain from ruin and laid the groundwork for an extraordinary economic renaissance. For critics, she was a heartless tyrant who ushered in an era of greed that kicked the weak out onto the streets and let the rich become filthy rich.
Thatcher had significant health problems in her later years, suffering several small strokes. She retired from public life after a stroke in 2002.
She was married to Denis Thatcher for nearly 52 years until his death in June 2003. The couple had twins, Mark and Carol.
The Associated Press contributed to this report.
