The former cabinet minister died this morning at his home in west London surrounded by family members.
In a statement his children Stephen, Hilary, Melissa and Joshua said: "It is with great sadness that we announce that our father Tony Benn died peacefully early this morning at his home in west London surrounded by his family.
"We would like to express our heartfelt thanks to all the NHS staff and carers who have looked after him with such kindness in hospital and at home.
"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.
"Arrangements for his funeral will be announced in due course."
Prime Minister David Cameron paid tribute to the Labour veteran on Twitter.
He said: "Tony Benn was a magnificent writer, speaker and campaigner. There was never a dull moment listening to him, even if you disagreed with him."
Labour MPs also took to the social network to pay warm tributes.
Former cabinet minister Peter Hain said: "Tony Benn was a giant of socialism who encouraged me to join Labour in 1977: wonderful inspirational speaker and person: will be deeply missed."
Diane Abbott said: "Admired so many things about Benn: unwavering principles; always open to new ideas; stellar political speaker but unfailingly courteous."
Barry Sheerman, who entered parliament in 1979 and served alongside Mr Benn for many years, said: "Sad news of Tony Benn death. I had my differences with him but he was a "big beast" in our political life and party history."
Lucy Powell, one of the party's newest MPs added: "Very sorry to hear the sad news about Tony Benn. He was a political giant of the last century, principled and passionate."
Labour leader Ed Miliband paid tribute 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.
"Tony Benn spoke his mind and spoke up for his values. Whether you agreed with him or disagreed with him, everyone knew where he stood and what he stood for.
"For someone of such strong views, often at odds with his party, he won respect from across the political spectrum.
"This was because of his unshakeable beliefs and his abiding determination that power and the powerful should be held to account.
"He believed in movements and mobilised people behind him for the causes he cared about, often unfashionable ones. In a world of politics that is often too small, he thought big about our country and our world.
"Above all, as I had cause to know, he was an incredibly kind man. I did work experience with him at the age of 16. I may have been just a teenager but he treated me as an equal. It was the nature of the man and the principle of his politics.
"I saw him for the last time a couple of weeks ago in hospital. He may have been ailing in body but was as sharp as ever in mind. As I left he said to me 'Well, old son. Let's have a proper talk when you have more time'.
"As he said of his wife Caroline at her funeral, he showed us how to live and how to die.
"All of my condolences go to his children Stephen, Hilary, Melissa and Joshua and his wider family. In their own ways, they are all a tribute to him as a father, a socialist, and a most decent human being."