Gartside was born in Cardiff, Wales, UK. His father died while he was a child, after which his widowed mother married a solicitor from Newport named Gordon Gartside, from whom Green adopted his new last name. He later became inspired to adopt the stage name "Green" after a train journey he took back to Wales, in which he looked out of the window and could only see the natural greenery of the area.
In the mid-1970s, Gartside moved to Leeds to study art at Leeds Polytechnic (now Leeds Metropolitan University). It was there that he formed the post-punk band Scritti Politti in 1977, with school friend Nial Jinks and university friend Tom Morley. After Gartside and Morley had left Leeds Polytechnic, they moved to London, later securing a recording deal with Rough Trade Records who released the first Scritti Politti album Songs to Remember in 1982. However, subsequent Scritti Politti albums featured Gartside with different personnel, with Gartside being the only constant member of the group. In 2012, Gartside, who has suffered from recurring stage fright that prevented Scritti Politti from touring for many years, performed several songs by Sandy Denny as part of a tribute called 'The Lady' that took place in several UK cities. He has also returned to touring with Scritti Politti.