Burnett, who went on to become an attorney after the band's heyday in the early 1960s, was suffering from a brain tumor when he died.
The Highwaymen hit No. 1 on the U.S. charts with their 1961 single "Michael, Row the Boat Ashore" and also scored hits with "All My Trials" and "Big Rock Candy Mountain."
"The original Highwaymen, along with the Kingston Trio and later, Peter Paul and Mary, were among those responsible for popularizing American music -- call it folk, blues, country, whatever," singer-songwriter Kris Kristofferson told the Los Angeles Times last year after lead singer Dave Fisher died.
The Times said the Highwaymen were formed by six freshmen at Wesleyan University in Connecticut, which put them a short commute from the thriving folk scene in New York's Greenwich Village. They went on to cut eight albums before breaking up in 1964 when Burnett and two other members decided to attend graduate school.