A Labour cabinet minister in the 1960s and 1970s, Benn had been seriously ill.
In a statement his children Stephen, Hilary, Melissa and Joshua said their father died peacefully at his home in west London surrounded by his family.
"We will miss above all his love which has sustained us throughout our lives. But we are comforted by the memory of his long, full and inspiring life and so proud of his devotion to helping others as he sought to change the world for the better," they said in a statement.
"He had a remarkable historical memory and experience. This is a man who was bounced on the knee, as a baby, of Mr Gandhi, the Indian independence leader," said Respect Party MP George Galloway in his tribute.
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Benn stood down from Parliament before the 2001 election in order, as he put it, "to spend more time on politics", and spearheaded campaign opposing to UK military involvement in Iraq and Afghanistan.
An ardent Left-winger, Benn became the first peer to renounce his aristocratic title to remain in the House of Commons.
Benn became an MP in November 1950 and served in the Cabinet under former British Prime Ministers Harold Wilson and James Callaghan.
A major figure on the left of the Labour party, he narrowly missed out on the deputy leadership in 1981 and went on to be a popular public speaker, anti-war campaigner and political diarist.
Labour leader Ed Miliband led the tributes to an "iconic figure of our age". He said: "He will be remembered as a champion of the powerless, a great parliamentarian and a conviction politician.
Prime Minister David Cameron said: "I am sorry to hear that Tony Benn has died.
"He was a magnificent writer, speaker, diarist and campaigner, with a strong record of public and political service. There was never a dull moment listening to him, even when you disagreed with everything he said.