A family statement said the parliamentary veteran – who spent 43 years as an MP – died after a short illness.
“Tam Dalyell devoted his life to public service in Scotland, in the UK, and beyond,” the statement said.
“He made an enormous contribution in many spheres. He will be much missed both publicly, and more importantly personally, by his family and many friends.”
Labour leader Jeremy Corbyn led tributes, describing him as a “titan of parliamentary scrutiny”, while First Minister Nicola Sturgeon said he was a “real giant” of Scottish politics. Former Labour prime minister Gordon Brown said: “For four decades Tam Dalyell was one of the truly great characters of Scottish political life. He was a leader – widely respected and admired for his insight, his integrity and his eloquence.”
Born in Edinburgh in 1932, Mr Dalyell grew up in the family home, the Binns, near Linlithgow, West Lothian. He was educated at the Edinburgh Academy, Eton and Cambridge before winning a by-election in West Lothian and entering the House of Commons as Labour MP. He inherited a baronetcy, but he never used the title.
Mr Dalyell, who backed Mr Corbyn in the battle for the Labour leadership, quickly became a member of the “awkward squad”, repeatedly raising questions over issues such as military action in a number of war zones including Iraq and Yugoslavia.
He was also outspoken about the Lockerbie disaster, refusing to blame Colonel Gaddafi.
He opposed devolution and raised the West Lothian Question – asking why Scottish MPs should have the right to vote on purely English legislation in the House of Commons after devolution, while English MPs would not be able to vote on Scottish matters.
His refusal to “toe the party line” meant he never achieved high office in his political career.
Scottish Conservative leader Ruth Davidson said he was “unique – thoughtful, gracious, dignified and utterly tenacious”.
Mr Corbyn said the late MP had been “fearless in pursuit of the truth”, fighting to expose official wrongdoing and cover-ups – from the miners’ strike to Iraq.
“The title of his autobiography summed Tam up to a tee: The Importance Of Being Awkward,” he said.
“But he was much more than that. Tam was an outstanding parliamentarian, a socialist and internationalist, and a champion of the underdog, here and abroad.”
Shadow chancellor John McDonnell said he was “a fine socialist and a parliamentarian of the first order”.
“He was a man of absolute principle, determined to speak truth to power and hold government to democratic account,” he said.
Scottish Labour leader Kezia Dugdale said: “The Labour movement has lost a giant. Tam Dalyell was one of the most influential MPs, writers and thinkers of his generation.”
In 1963, he married Kathleen, the elder daughter of the late Baron Wheatley, one-time Lord Advocate and a former Labour MP for East Edinburgh. They had a son and a daughter.
His final book The Question of Scotland – Devolution And After, was published last year.