Nash, whose health had been in decline, died at his home of natural causes on Tuesday, his son told US media.
The musician began singing as a child and made his major label debut with the 1957 song A Teenager Sings the Blues.
Nash, born in Houston, was one of the first non-Jamaican singers to record reggae music in Kingston, Jamaica.
His single I Can See Clearly Now sold more than a million copies and reached the top of the Billboard Hot 100 chart in 1972, where it remained for four weeks.
He also had a number one hit in the UK in 1975 with Tears on My Pillow.
According to his official website, Nash helped reggae legend Bob Marley sign a recording contract.
Nash's covers of songs like Stir It Up helped bring Marley's music to a broader audience, and the pair later collaborated on a track called You Poured Sugar On Me.