Mr Salmond described the politician, who was an MP for more than 50 years, as an "outstanding figure" who had been a great support to him.
Scottish Labour leader Johann Lamont also praised the Labour Party grandee as "an amazing life at the heart of British politics".
The veteran left-wing politician and campaigner died on Friday morning at his home in London.
His death was announced in a statement released by his children, who said he had been surrounded by family at his passing.
Mr Salmond said: "Tony Benn was an outstanding figure whose career encompassed several political generations.
"Like many young parliamentarians I found Tony Benn supportive and helpful, regardless of political differences, and it was on his unfailing courtesy to opponents that much of his cross-party respect was founded.
"His political reputation will transcend the internal Labour Party battles of the seventies and eighties and be founded instead on a politician whose writings and campaigning reinvigorated grass roots politics."
Tributes poured in from all sides of the political divide as news of Mr Benn's death broke yesterday.
Mr Benn, who retired from Parliament in 2001, will be remembered in Scotland for his role in the campaign to save the Upper Clyde shipyards from closure in the early 1970s.
He was also a prolific speaker on the lecture circuit, filling Glasgow's Royal Concert Hall in January 2013.
Scottish Labour leader Johann Lamont MSP, said: "This is sad day but we can all celebrate an amazing life at the heart of British politics and public life.
"Whether you agreed with him or not, Tony Benn was always compelling, interesting and entertaining, with unshakeable beliefs and a clear sense of right and wrong.
Tony was a giant of the Labour movement when I first joined the party and we were wrestling with big ideas about our future direction.
"But even in his later years, he remained relevant and influential with his wit and wisdom on a range of issues, from international affairs to Scottish devolution.
"Above all, he was a dedicated family man and our thoughts are with those who feel his loss the most at this time."
Councillor Gordon Matheson, leader of Glasgow City Council, said: "I share the sadness felt by so many others at the passing of Tony Benn.
"He's regarded as a political hero by many across the Labour movement in Glasgow, and was widely respected by those who didn't necessarily share his views. He was actively supportive of many campaigns in the city, from the shipyard work-in to anti-war protests.
"I particularly remember hearing him speak at May Day on Glasgow Green.
"His one-man 'audience with' show at the Citizens Theatre demonstrated his breath of knowledge, and his relaxed and respectful style when engaging with the general public.
"He'll be missed and remembered, and on behalf of Glasgow Labour I wish to pass on my condolences to his beloved family."
In Bristol, a book of condolence has been opened for Mr Benn in City Hall, close to a statute of the former city MP.
Mayor George Ferguson said: "Tony Benn was undoubtedly the most remarkable politician to represent a Bristol constituency since Edmund Burke.
"He was a great orator and I always admired him on a personal level and stood side by side with him on such issues as human and civil rights.