Solicitors acting on behalf of his family said in a statement: "It is with great sadness that the family of Peter Green announce his death this weekend, peacefully in his sleep.
"A further statement will be provided in the coming days."
Green, from Bethnal Green in east London, formed Fleetwood Mac with drummer Mick Fleetwood in 1967.
They came together after Green's stint filling in for Eric Clapton in John Mayall's Bluesbreakers. Green and Fleetwood then convinced John McVie to join the band as bass guitarist, in part by naming the band Fleetwood Mac.
He wrote the instantly recognisable instrumental track Albatross, which remains the band's only number one hit, plus two other early hits, Black Magic Woman and Oh Well. And it was under Green's direction that they produced their first three albums.
The band's debut album was released in 1968. Simply called Fleetwood Mac, but also known as Peter Green's Fleetwood Mac, it gained widespread acclaim and reached number four in the charts.
Green left the band after a last performance in 1970 as he struggled with his mental health. He was eventually diagnosed with schizophrenia and spent time in hospital in the mid-70s.
He married Jane Samuels in January 1978. They divorced in 1979 and share a daughter.
Green was among the eight members of the band - along with Fleetwood, Stevie Nicks, Lindsey Buckingham, John McVie, Christine McVie, Danny Kirwan and Jeremy Spencer - who were inducted into the Rock & Roll Hall of Fame in 1998.
The news of his death comes days after Fleetwood Mac announced they would release a retrospective box set documenting the band's early years between 1969 and 1974.
Success is not final, failure is not fatal. It is the courage to continue that counts.