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.
He was the focus of BBC Two's How to Be a Composer, in which he spent a year at the Royal Academy of Music attempting to learn to compose classical music, despite being unable to read music or play an instrument.
Morley is the author of Words and Music: the history of pop in the shape of a city. The book is a journey through the history of pop; it seeks to trace the connection between Alvin Lucier's experimental audio recording, "I Am Sitting in a Room" and Kylie Minogue's "Can't Get You Out of My Head". A synthetic Kylie features as the central character of the book. The book was later turned into the hour-long epic musical track "Raiding the 20th Century" by DJ Food, which features Morley reading from his book and speculating on the cultural significance of the mashup, amidst the sounds of those very mashups.
His other books include Ask: The Chatter of Pop (a collection of his music journalism) and Nothing, concerning his father's suicide and that of Joy Division singer Ian Curtis and such unhappy experience as the time Morley spent at Stockport Grammar School.
Morley teamed up with the Auteurs' James Banbury to form the band Infantjoy and in 2005 released an album entitled Where the Night Goes on Sony BMG. With, an album featuring collaborations with Tunng, Isan and other musicians, was released in October 2006 on Morley and Banbury's own label ServiceAV.
Morley is a lifelong fan of the jazz musician John Surman and conducted an interview with the artist for The Guardian newspaper.
Morley was married to Claudia Brücken with whom he has a son and a daughter.
He is the brother of filmmaker Carol Morley.