Morley was born in Farnham, Surrey, and moved with his family to Eccles, Salford, before starting school. He was educated at Stockport Grammar School, at the time a direct grant grammar school, and the Royal Academy of Music.
Morley wrote for three Manchester area magazines in the late 1970s, Penetration, Out There and Girl Trouble. He then went on to write for NME, where he and colleagues such as Ian Penman developed an innovative style of music criticism that drew on critical theory and other non-musical sources. After leaving the NME, he was a regular contributor to BLITZ magazine from 1984 to 1987, penning a monthly television column as well as a series of interviews.
For a period of time, Morley produced and managed Manchester punk band the Drones. However, he first came to wider attention with a brief appearance in the video for ABC's "The Look of Love" (in which he mimes the words "what's that?" in a call-and-response routine with singer Martin Fry), and some fame as co-founder, with Trevor Horn, of ZTT Records and electronic group Art of Noise.
Morley is credited with steering the marketing and promotion of the phenomenal early success of ZTT's biggest act, Frankie Goes to Hollywood, heavily influenced by Deutsch Amerikanische Freundschaft's image for Alles Ist Gut. Although it has never been confirmed, it is claimed that Morley authored the provocative slogans on the band's T-shirts (e.g. "Frankie Say Arm the Unemployed", "Frankie Say War! Hide Yourself").
He was the first presenter of BBC Two's The Late Show, and has appeared as a music pundit on a number of other programmes. For the short-lived Channel 4 arts strand Without Walls he wrote and presented a documentary on boredom. Morley regularly appeared on BBC's The Review Show.