Mr Brown hailed him as "a man of deep principle and passionate idealism" who fought all his life for his beliefs and for the Labour Party.
Mr Foot died shortly before 7am this morning at his home in Hampstead, north London. He had been ill for some time and had been receiving 24-hour care.
His death was announced to the House of Commons by Justice Secretary Jack Straw, who told MPs the news would be received "with great sadness not only in my own party but across the country as a whole".
A member of a prominent Liberal family, Mr Foot joined Labour in the 1930s and worked as a journalist for left-wing publications New Statesman and Tribune, before being appointed editor of the Evening Standard by Lord Beaverbrook in 1942.
He entered Parliament in 1945 and went on to become a hero of the left, championing nuclear disarmament and campaigning against British membership of the European Economic Community in the 1975 referendum.
He became Labour leader in 1980, defeating the candidate of the right, Denis Healey, and led the party to its worst election defeat in 60 years in 1983.
But today he was remembered more for his sparkling oratory and political idealism.
Mr Brown said: "Michael Foot was a man of deep principle and passionate idealism and one of the most eloquent speakers Britain has ever heard.
"He was an indomitable figure who always stood up for his beliefs and whether people agreed with him or not they admired his character and his steadfastness.
"The respect he earned over a long life of service means that, across our country today, people, no matter their political views, will mourn the passing of a great and compassionate man."
Lord Healey, who served as Foot's deputy from 1980-83, said he was "very, very sorry to hear of his death".
Lord Healey said: "I was a great admirer of Michael's. He was a brilliant speaker.
"Although we disagreed very much over policy, I was very glad to serve under him as deputy leader.
"I don't think he should be remembered only for the 1983 election defeat, because he made a tremendous contribution to the Labour Party when its future was on a knife edge."
Labour former deputy prime minister John Prescott said in a message via Twitter: "So sad to hear about Michael Foot.
"A great man has died. He was the heart of our movement."
And Tony Benn, who stood against Mr Healey - now Lord Healey - for the deputy leadership in 1981 despite Mr Foot's appeal for him to avoid a divisive battle, also paid tribute.
Mr Benn told Sky News: "He was a very formidable writer and a very powerful speaker, electrifying audiences.
"He was a great credit to the Labour movement. I know he did not win the election, but the fact that he became leader and fought the election puts him in the top list of figures in the history of the party."
Conservative leader David Cameron said Mr Foot was a "very intelligent, witty, amusing and thoughtful man".
"He was a brilliant speaker," the Tory leader told talkSPORT radio. "I'm obviously not old enough to have been in the House of Commons at the same time, but reading some of his speeches, (they) were incredibly powerful.
"He had an extraordinary life but they will be mourning the death of a remarkable man."
Labour Party general secretary Ray Collins said: "Michael Foot's passing is very sad news for the Labour Party and the wider movement. As leader of our party, a Labour minister, a writer and a man, he was a tireless campaigner for social justice, whose intelligence, charm and courage will be remembered for years to come."
Mr Foot first became MP for Plymouth Devonport in 1945, before becoming MP for Ebbw Vale and Blaenau Gwent.
He was employment secretary in the 1974/76 Labour government under Harold Wilson and went on to become leader of the Commons between 1976 and the 1979 general election.
His election as leader in 1980 followed Labour's defeat at the hands of Margaret Thatcher and marked one of the most difficult periods in the party's history, when it was almost torn apart by left-right infighting and the defection of several senior figures to form the Social Democratic Party (SDP).
Labour's manifesto for the 1983 election - advocating unilateral nuclear disarmament, abolition of the House of Lords, and quitting the EEC - was famously dubbed the "longest suicide note in history". The party went down to ignominious defeat with just 27% of the vote.
Mr Foot was famously derided for wearing what was characterised as a donkey jacket at a Cenotaph remembrance ceremony, although he always insisted he had sported a smart car coat.
Although his appearance was often mocked, his oratory inside and outside the Commons was famed.
He was succeeded as Labour leader by his protege and fellow Welshman Neil Kinnock, who took on the hard left and sowed the seeds of New Labour.
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