WKRN-TV, Nashville, and The Tennessean newspaper said Welch's wife discovered the Los Angeles-born musician with a gunshot wound to his chest at their home in Antioch.
Police spokesman Don Aaron told Billboard.com Welch had a history of health issues and left a suicide note.
Welch joined Fleetwood Mac in 1971, playing guitar and singing on five albums.
After leaving the band, he enjoyed success as a solo artist. His platinum-selling 1977 album "French Kiss" featured the hits "Sentimental Lady," "Ebony Eyes" and "Hot Love, Cold World."