The 73-year-old singer - who co-founded Fleetwood Mac alongside Peter - remembered his bandmate as "monumental".
He said in a statement: "For me, and every past and present member of Fleetwood Mac, losing Peter Green is monumental. Peter was the man who started the band Fleetwood Mac along with myself, John McVie, and Jeremy Spencer. No one has ever stepped into the ranks of Fleetwood Mac without a reverence for Peter Green and his talent, and to the fact that music should shine bright and always be delivered with uncompromising passion ... Peter, I will miss you, but rest easy your music lives on. I thank you for asking me to be your drummer all those years ago. We did good, and trail blazed one hell of a musical road for so many to enjoy. God speed to you, my dearest friend ... Love Mick Fleetwood."
It was confirmed Peter died in his sleep aged 73.
The statement from Swan Turton solicitors said: "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."
Peter Green was born in Bethnal Green in east London, and he formed Fleetwood Mac alongside drummer Mick Fleetwood in the late 1960s. He left the band a few years later in 1970 due to mental health problems.
He was later diagnosed with schizophrenia.
Peter and Fleetwood Mac's early years were celebrated at a recent gig at the London Palladium, attended by Mick Fleetwood, Pink Floyd's David Gilmour, ZZ Top's Billy Gibbons as well as guitarists Jonny Lang and Andy Fairweather Low.