The waltzing song, originally recorded by Little Willie John in 1955, features a home-recorded vocal that Green tracked in 1968 with a tape recorder.
The revamped “Need Your Love So Bad” is one of two songs connected to The Albatross Man, an upcoming book chronicling Green’s life and career.
“For the past four years Peter worked directly with Rufus Publications to produce a huge, illustrated visual book of his life and career,” the book’s publisher explained in a statement.
In February 2020, Gilmour took part in an all-star Green tribute concert that also featured Hammett, Neil Finn, Noel Gallagher, Billy Gibbons, John Mayall, Christine McVie, Jeremy Spencer, Zak Starkey, Pete Townshend, Steven Tyler and Bill Wyman.