Police said Welch's body was found by his wife Wendy with a single gunshot wound to the chest, and he had left a suicide note. Welch suffered from health problems, but police did not disclose what those issues were.
Mick Fleetwood, one of the founding members of Fleetwood Mac and Welch's manager during his solo career, had remained in close contact with his former band mate over the years and told Reuters that Welch's suicide was "incredibly out of character."
"He was a very, very profoundly intelligent human being and always in good humor, which is why this is so unbelievably shocking," he said.
"He was a huge part of our history which sometimes gets forgotten ... mostly his legacy would be his songwriting abilities that he brought to Fleetwood Mac, which will survive all of us," Fleetwood said.
"If you look into our musical history, you'll see a huge period that was completely ensconced in Bob's work."
Welch is the second member of Fleetwood Mac to die this year. In January, another former guitarist for the band, Bob Weston, died in London from a gastrointestinal hemorrhage, at the age of 64.
Welch was born on Aug. 31, 1945 in Los Angeles to movie producer father Robert L. Welch and actress mother Templeton Fox. He moved to Paris to study French at the Sorbonne, and then returned to Los Angeles in the early 1970s.
He was invited to join Fleetwood Mac after the departure of founding members Peter Green and Jeremy Spencer.
He played guitar and was a vocalist with the band from 1971 to 1974, working on five of their early albums including 1971's Future Games, 1972's Bare Trees and 1973's Mystery to Me.
It was after Welch's departure from the band in 1975 that Fleetwood Mac went on to find its largest measure of fame on albums such as 1977's Rumours with the addition of Lindsey Buckingham and Stevie Nicks to the band's lineup.
Nicks released a statement, calling Welch's death "devastating."
"He was an amazing guitar player - he was funny, sweet - and he was smart - I'm so very sorry for his family and for the family of Fleetwood Mac - so, so sad," Nicks said.
Welch fell out with his former band mates after suing the group in 1994 for unpaid royalties, which led to his exclusion from the group's Rock and Roll Hall of Fame induction in 1998.
The singer and guitarist formed a hard rock group called Paris in 1975, releasing two albums, Paris and Hunt Sales, before disbanding the group a few years later and embarking on a solo career.
His debut solo record, the pop-driven French Kiss in 1977, went platinum and produced the hits Sentimental Lady, Ebony Eyes and Hot Love, Cold World. Welch followed up with 1979's Three Hearts, and four more albums throughout the early 1980s, none of which emulated the same success as French Kiss.
He moved to Phoenix, Arizona, in 1987 and formed a short-lived group called Avenue M, before moving to Nashville in the late 1990s, working on a songwriting career and releasing a tribute to bebop music, Bob Welch Looks At Bop, in 1999.
His most recent albums, 2003's His Fleetwood Mac Years and Beyond and 2006's His Fleetwood Mac Years and Beyond 2, had previously unreleased material as well as new compositions.
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It says a lot about ET when someone's death is reported under 'gossip'. Even cheap tabloids aren't this insensitive.