A native of Birmingham, Green was involved in the city's post-punk and goth scenes in early 1980s and was close friends with musicians such as Paul Neville and Diarmuid Dalton. He formed his first band, OPD (Officially Pronounced Dead), in 1982 with Neville. The band usually rehearsed at Green's house or Nevilles house. They changed their name to Fall of Because after the Killing Joke song of the same name in 1985. Initially they used a basic drum machine, with Neville playing guitar, and Green on bass and vocals, and were writing songs influenced by The Cures' 17 Seconds and Faith albums. After meeting a 15-year-old Justin Broadrick in 1984 outside their local council estate shops, above which Broadrick lived with his parents, they started their friendship over their mutual admiration for the Stranglers, and other punk bands. Soon, Broadrick started playing drums in the band, and the three of them began writing songs that were influenced by bands such as Swans and Sonic Youth, whilst still retaining the psychedelic overtones that was inherent in the earlier Fall of Because music. Green was also introduced to various artists such as Throbbing Gristle, Whitehouse and SPK at this time, by Broadrick.
In 1986 they recorded a demo, Extirpate, at Rich Bitch studios in Birmingham, and sold a few copies to friends and other musicians in Birmingham. The band also played several gigs at The Mermaid public house in Birmingham with the likes of Napalm Death, Heresy, Amebix. In 1987 Broadrick left Fall of Because to join Head of David. When Broadrick was sacked from Head of David in 1988, he and Green, who were sharing a flat together at the time, formed Godflesh. Throughout its career, Godflesh has released eight records and pioneered the industrial metal genre. After recording Godflesh's sixth album, Hymns, in October 2001, he left Godflesh. He was replaced by Prong bassist Paul Raven. Nevertheless, the band disbanded in 2002 in the midst of their European tour. In following years, Green, who supported himself with various professions, disappeared from the music scene until 2010.
Green's only solo album, I-VII, was released under his Vitriol moniker in 1998 through Neurot Recordings. It was recorded in 1995.
Green was married in 2010. Green and Broadrick also reunited Godflesh in 2010 and began touring. The band's seventh album, and the first since the reunion, A World Lit Only by Fire, was released in 2014. Their eighth album, Post Self, followed in 2017.
Green is scheduled to make his solo debut as Vitriol on 8 December, 2018 at Hospital Fest 2018 in Queens, New York, twenty years after the Vitriol album was first released.