Lady Thatcher, born Margaret Roberts, was the first female prime minister, a role she held from 1979 to 1990.
Prime Minister David Cameron led the tributes, describing her as "a great leader, a great prime minister and a great Briton".
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 was born on 13 October 1925 in Grantham, Lincolnshire. Her father, Alfred Roberts, was a grocer, Methodist lay preacher and local councillor.
She is to receive a ceremonial funeral with military honours at St Paul's Cathedral.
The Archbishop of Canterbury, the Most Reverend Justin Welby said in a statement: "It was with sadness that I heard the news of the death of Baroness Thatcher and my prayers are with her son and daughter, her grandchildren, family and friends. It is right that today we give thanks for a life devoted to public service, acknowledging also the faith that inspired and sustained her."
The head of the Catholic Church in England and Wales, Archbishop Vincent Nichols said: "It was with sadness that we heard the news of the death of Baroness Thatcher, who served this country for many years both as a Member of Parliament and as Prime Minster.
"We pray for the repose of her soul and for the intentions of her family and all those who now mourn for her."
The President of the Methodist Conference, the Reverend Dr Mark Wakelin said: "Margaret Thatcher was a hugely significant, complex and yet divisive figure in post-war British politics. She achieved a major breakthrough as Britain's first woman Prime Minister, and her time in office fundamentally changed the nature of British society, especially the relationship between individuals and the state.
"For many people she was a courageous and committed leader, and one of the best known British politicians around the world - her roots in a personally responsible Methodist tradition were greatly admired by many.
"Perhaps one of her greater achievements was to change the post-war political consensus, forcing her political rivals to campaign far more on her terms."
Albert Mohler, president of Southern Baptist Theological Seminary said Thatcher was one of the "greatest leaders of the twentieth century".
"Margaret Thatcher was a model of convictional leadership. She led with intellectual principles and ideas. She saw leadership as an adventure," he said.
The responses have not all been positive though. Simon Barrow, of Ekklesia think tank, tweeted: "Condolences to the #Thatcher family, but also to the many victims of her unjust policies, which are being continued by the coalition today."
Others hinted at a more conciliatory tone from commentators.
Premier Christian Radio presenter Maria Rodrigues-Toth tweeted: "Before casting a stone at someone for the choices they made during their life, remember that u r not perfect yourself. #Thatcher."