Delerue was born 12 March 1925 in Roubaix, France, to Georges Delerue and Marie Lhoest. He was raised in a musical household; his grandfather led an amateur chorale group and his mother sang and played piano at family gatherings. By the age of fourteen he was playing clarinet at the local music conservatory. In 1940 he was forced to abandon his studies at the Turgot Institute in order to work at a factory to help support his family. He continued playing clarinet with local bands, eventually transitioning to piano under the instruction of Madame Picavet-Bacquart. He studied Bach, Mozart, Beethoven, Chopin, and Grieg, and was particularly inspired by Richard Strauss. Following a long convalescence after being diagnosed with scoliosis, Georges decided to become a composer.
In 1945, following his studies at the Roubaix conservatory, Delerue was accepted into the Conservatoire de Paris, where he studied fugue with Simone Plé-Caussade and composition with Henri Büsser. To help support himself, he took jobs playing at dances, baptisms, marriages, and funerals—even performing jazz in the piano bars near the Paris Opera.
In 1947 he received an honorable mention for the Rome Prize, and the following year he won the Second Grand Rome Prize. That year at the Theater Festival of Avignon, Delerue conducted a performance of Scheherazade. In the 1949 Rome Prize competition, he won the First Second Grand Prize, and the First Prize for Composition. He began writing stage music during the late 1940s, including for the Théâtre National Populaire, Comédie-Française and the company of Jean-Louis Barrault. He also became friends with Maurice Jarre and Pierre Boulez.