In 1962, Greenaway began studies at Walthamstow College of Art, where a fellow student was musician Ian Dury (later cast in The Cook, the Thief, His Wife & Her Lover). Greenaway trained as a muralist for three years; he made his first film, Death of Sentiment, a churchyard furniture essay filmed in four large London cemeteries. In 1965, he joined the Central Office of Information (COI), working there fifteen years as a film Editor and Director. In that time he created a filmography of experimental films, starting with Train (1966), footage of the last steam trains at Waterloo station (situated behind the COI), edited to a musique concrète composition. Tree (1966), is a homage to the embattled tree growing in concrete outside the Royal Festival Hall on the South Bank in London. By the 1970s he was confident and ambitious and made Vertical Features Remake and A Walk Through H. The former is an examination of various arithmetical editing structures, and the latter is a journey through the maps of a fictitious country.
In 1980, Greenaway delivered The Falls (his first feature-length film) – a mammoth, fantastical, absurdist encyclopaedia of flight-associated material all relating to ninety-two victims of what is referred to as the Violent Unknown Event (VUE). In the 1980s, Greenaway's cinema flowered in his best-known films, The Draughtsman's Contract (1982), A Zed & Two Noughts (1985), The Belly of an Architect (1987), Drowning by Numbers (1988), and his most successful (and controversial) film, The Cook, the Thief, His Wife & Her Lover (1989). Greenaway's most familiar musical collaborator during this period is Composer Michael Nyman, who has scored several films.
In 1989, he collaborated with Artist Tom Phillips on a television serial A TV Dante, dramatising the first few cantos of Dante's Inferno. In the 1990s, he presented Prospero's Books (1991), the controversial The Baby of Mâcon (1993), The Pillow Book (1996), and 8½ Women (1999).
In the early 1990s, Greenaway wrote ten opera libretti known as the Death of a Composer series, dealing with the commonalities of the deaths of ten composers from Anton Webern to John Lennon, however, the other composers are fictitious, and one is a character from The Falls. In 1995, Louis Andriessen completed the sixth libretto, Rosa – A Horse Drama. He is currently professor of cinema studies at the European Graduate School in Saas-Fee, Switzerland.
On 17 June 2005, Greenaway appeared for his first VJ performance during an art club evening in Amsterdam, Netherlands, with music by DJ Serge Dodwell (aka Radar), as a backdrop, 'VJ' Greenaway used for his set a special system consisting of a large plasma screen with laser controlled touchscreen to project the ninety-two Tulse Luper stories on the twelve screens of "Club 11", mixing the images live. This was later reprised at the Optronica festival, London.
On 12 October 2007, he created the multimedia installation Peopling the Palaces at Venaria Reale at the Royal Palace of Venaria that animates the Palace with 100 videoprojectors.
In 2006, Greenaway began a series of digital video installations, Nine Classical Paintings Revisited, with his exploration of Rembrandt's Night Watch in the Rijksmuseum in Amsterdam. On 30 June 2008, after much negotiation, Greenaway staged a one-night performance 'remixing' da Vinci's The Last Supper in the refectory of Santa Maria delle Grazie in Milan to a select audience of dignitaries. The performance consisted of superimposing digital imagery and projections onto the painting with music from the Composer Marco Robino.
Greenaway exhibited his digital exploration of The Wedding at Cana by Paolo Veronese as part of the 2009 Venice Biennial. An arts Writer for The New York Times called it "possibly the best unmanned art history lecture you'll ever experience," while acknowledging that some viewers might respond to it as "mediocre art, Disneyfied kitsch or a flamboyant denigration of site-specific video installation." The 50-minute presentation, set to a Soundtrack, incorporates closeup images of faces from the painting along with animated diagrams revealing compositional relations among the figures. These images are projected onto and around the replica of the painting that now stands at the original site, within the Palladian architecture of the Benedictine refectory on San Giorgio Maggiore. The Soundtrack features music and imagined dialogue scripted by Greenaway for the 126 "wedding guests, servants, onlookers and wedding crashers" depicted in the painting, consisting of small talk and banal chatter that culminates in reaction to the miraculous transformation of water to wine, according to the Gospels the first miracle performed by Jesus. Picasso's Guernica, Seurat's Grande Jatte, works by Jackson Pollock and Claude Monet, Velázquez's Las Meninas and Michelangelo's The Last Judgment are possible series subjects.
Greenaway was interviewed for Clive Meyer's Critical Cinema: Beyond the Theory of Practice (2011), and voiced strong criticisms of film theory as distinct from discussions of other media: "Are you sufficiently happy with cinema as a thinking medium if you are only talking to one person?"
On 3 May 2016, he received a Honoris Causa doctorate from the University of San Martín, Argentina.