Piper was born in Epsom, Surrey in 1903. A talented writer and artist from an early age, he kept topographical and architectural notebooks and illustrated his own privately printed books of poetry. Reluctantly, he became an articled clerk in the office of his solicitor father (1921-26), leaving to study art on his father's death. Following his study under Raymond Coxon at Richmond College of Art (1926), Piper held his first exhibition (of wood engravings) at the Arlington Galleries. He then attended the Royal College of Art, where he studied painting under Maurice Kestleman and lithography and stained glass under Francis Spear (1927-29). He left the Royal College early, in order to marry Eileen Holding, who had been a fellow student at Richmond. He earned his living writing art and theatre criticism for the Listener and the New Statesman, and spent time painting and making stained glass. However, he soon met Myfanwy Evans at the Suffolk home of his friend Ivon Hitchens, and dissolved his first marriage in order to marry her.
Elected to the London Group (1933) and 7 & 5 Society (1934), Piper began to take an active interest in Modernism. He made constructions and collages which show the influence of Ben Nicholson and, with Myfanwy Evans, co-edited Axis, the pioneering journal of abstract art (1935-37).
Piper spent much time working over the established categories of British landscape. Instrumental in reviewing notions of 'Englishness', he wrote British Romantic Artists (1942), and was an ideal choice for involvement in Recording Britain (1940) and as an Official War Artist (1944). During the Second World War he painted bombed churches and would later revitalise many buildings with his stained glass (from 1954) and tapestries (from 1966). From before the war he was already an important muralist and stage designer, producing the curtain for the first definitive performance of Sitwell & Walton's Façade (29 May 1942) and a notable series of settings for the operas of Benjamin Britten (from The Rape of Lucretia, 1946).
In later years, Piper took a number of official roles, serving as a Trustee for both the National and Tate galleries and sitting on the Oxford Diocesan Advisory Committee, the Royal Fine Art Commission and the Arts Council panel. As a reward for such work, and for a lifetime's achievement as an artist, he was made a Companion of Honour (1972). Major retrospectives were held at the Museum of Modern Art, Oxford (1979) and the Tate Gallery (1983). He died at Fawley Bottom, Oxfordshire on the 27 June 1992.