Police spokesman Don Aaron said Welch's wife found him with a chest wound at their south Nashville home around 12:15 p.m.
Welch was a guitarist and vocalist for Fleetwood Mac from 1971 to 1974. He formed the British rock group Paris in 1976, and had hits including "Sentimental Lady" in 1977 and "Ebony Eyes" in 1978. Fleetwood Mac's Christine McVie and Lindsey Buckingham did backing vocals on "Sentimental Lady."
Aaron said Welch apparently had had health issues recently. He said a suicide note was left.
Fleetwood Mac's career took off in the mid-1970s after Welch left the band. "Dreams" was a No. 1 hit in 1977 and "Don't Stop" the same year. It later became the anthem for Bill Clinton's presidential campaign. "Hold Me" was a hit in 1982 and "Little Lies" in 1987.
Welch, a native of Los Angeles, scored his biggest hit with "Sentimental Lady," which reached No. 8 on the Billboard chart. His other singles included "Precious Love" in 1979 and "Hot Love, Cold World" in 1978.
When Fleetwood Mac was inducted into the Rock and Roll Hall of Fame in 1998, Welch was not included in the group.
"It basically comes down to the fact that they don't like me anymore," he told The Plain Dealer of Cleveland at the time. "I guess they can do what they want. I could understand it if I had been a sideman for a year. But I was an integral part of that band ... I put more of myself into that band than anything else I've ever done."
Longtime Fleetwood Mac singer Stevie Nicks told The Associated Press that Welch's death hit her hard.
"The death of Bob Welch is devastating ... I had many great times with him after Lindsey and I joined Fleetwood Mac. He was an amazing guitar player - he was funny, sweet - and he was smart. I am so very sorry for his family and for the family of Fleetwood Mac - so, so sad ..."
Founding member Mick Fleetwood did not immediately respond to e-mails for comment Thursday.
As a songwriter, Welch had his songs recorded by Kenny Rogers, Sammy Hagar, the Pointer Sisters and others.
In 1999 he released a CD, "Bob Welch Looks at Bop," a salute to bebop music in the 1940s.
In an interview with The Tennessean in 2003, Welch said he never dreamed he'd be remembered for much.
"I just wanted to play guitar in a good band," he said. "I wanted to make the music I love. I wanted to travel the world and have adventures."
Welch also said "music is disposable now. It doesn't have the emotional impact anymore. That's sad."
He had lived in Nashville since the 1990s.
AP Music Writer Nekesa Moody contributed to this story.