Jean Redpath, who was born in Edinburgh and raised in Fife, passed away in an Arizona hospice.
After studying at Edinburgh University, she arrived in Greenwich Village, New York, in 1961, then at the hub of a folk revival. There, she shared a flat with Dylan and other future stars, including Rambling Jack Elliot.
After winning a rave review in the New York Times, she was offered recording deals and would go on to tour throughout the world, performing in venues including the Sydney Opera House.
A huge champion of Scottish folk and the songs of Robert Burns, in 1979 she was appointed as the first artist-in-residence at Stirling University and in 2011, returned to Edinburgh University to become artist-in-residence at its Department of Celtic and Scottish Studies. She was awarded the MBE in 1987.
Tributes have been paid to her on social media.
Former First Minister Lord McConnell said Redpath "was and remains a legend of folk music and a terrific cultural champion. Sorry to hear she has passed away."
Councillor Susan Aitken, the leader of the SNP Group on Glasgow City Council said she was saddened to learn of the death of the "wonderful" singer. She added: "She set new standard for singing Burns songs & made them feel vital & relevant to modern Scots."
Digital project manager Sara Christie tweeted: So sad to hear the great Jean Redpath has gone to the house of song in the sky. Her amazing voice has inspired so many. RIP."
Roddy Macdonald tweeted: "RIP Jean Redpath only you could read a recipe to an old hymn tune & make something hilarious & musically magnificent."