The son of amateur artists (his mother was a pianist; his father, a painter), André Jolivet was born in Paris in 1905 and began studying piano and music theory in 1909 with Henriette Fleurmann. He then briefly tried the clarinet and then, more seriously, the cello (around 1918); around the same time he joined the musical circle of the Church of Notre-Dame-de-Clignancourt, directed by Father Théodas. Jolivet was a school teacher in the city of Paris from 1924 to 1942, and at the same time followed his musical calling from a young age. He studied music theory and orchestration with Paul Le Flem (1927-1932), and composition with Edgard Varèse (1929-1933).

In 1931, Jolivet composed a String Quartet (his "school tribute" - testament scolaire, revised 1934), and one of his compositions was performed in public for the first time: his Trois Temps n°1 for piano premiered in a performance at the Société Nationale de Musique (SNM). After that, he was a regular guest of the SNM (notably, his Cinq incantations for flute were performed there), and participated in the creation of two concert societies, La Spirale (1935-1937), at whose first concert his Mana was premiered, and Jeune-France (founded in 1936 with Yves Baudrier, Daniel-Lesur, and Olivier Messiaen). At this time he began formalizing and disseminating his aesthetic approach, which was built on his left-wing political involvement, in lectures and articles.

After a first marriage to the violinist Martine Barbillon (1929), with whom he had a daughter, Françoise-Martine (born in 1930), in 1933 Jolivet married Sarah Hilda Ghuighui, with whom he had three children — Pierre-Alain (1935), Christine (1940), and Merri (1943). Hilda, who was Jewish, had survived the Second World War under the anti-semitic laws of France's Vichy government. André, returning from his military service (an experience that inspired Les Trois Complaintes du Soldat), nevertheless continued to forge a place for himself in French musical circles. A member of the Association de Musique Contemporaine (1940) and the Groupement des Compositeurs de Paris (1943), he composed the ballet Guignol et Pandore for the Opéra de Paris (1944), sat on juries at the Conservatoire de Paris (for the flute section, for which he composed Le Chant de Linos in 1944), wrote a book on Beethoven (published in 1955) and worked from time to time for the Comédie-Française, for which he composed and had his first experiences as an orchestra conductor (Le Soulier de satin, 1943). He was elected musical director of the Comédie-Française, a position he held from 1945-1959. After 1945, he conducted performances around the world.

It was after World War II that Jolivet gained a wide national and international reputation. He was a prolific composer for all formations, ranging from solo pieces (two Sonatas for piano, 1945 and 1957; Cinq Eglogues for viola, 1967; Ascèses for clarinet, 1967) to orchestral compositions (12 concertos for various instruments, 1948-1972; three Symphonies, 1953, 1959, and 1964), as well as chamber pieces (Rhapsodie à sept, 1957; Cérémonial for percussions, 1966), and vocal works (Epithalame, 1953; La Vérité de Jeanne, 1956; Le Cœur de la matière, 1965). Jolivet also composed stage pieces, for dance and theater performances. Among other places, he traveled to Austria and Hungary (1949), to the United States (1960, 1964), to Japan (1959, 1970), and to the U.S.S.R. (8 concert tours between 1966 and 1974), a testament to his renown outside of France. His success, highlighted by seven Grands Prix du Disque was punctuated by a few scandals, for example, the turbulent premieres of the symphony pieces Cinq danses rituelles in 1944 and Concerto for piano in 1951.

Jolivet was also involved in certain distribution and promotional organizations – he was president of the Association des Concerts Lamoureux (1962-1968) – and advocated for musicians' working conditions. In 1965, he was made honorary president of the Syndicat National des Artistes Musiciens and elected president of the Fédération Nationale du Spectacle-C.G.T., two performers' unions, and with them participated in the May 1968 protests.

Jolivet was a Chevalier de la Légion d’Honneur (1955) and Commandeur dans l’Ordre National du Mérite et des Lettres (1973), served as a technical advisor to the French Ministry of Cultural Affairs (1959-1962), and in 1962 was a member of the Commission for the IV^th and V^th Plans (French governmental planning commissions). In 1959, he founded the Centre Français d’Humanisme Musical, a composition and performance workshop located in Aix-en-Provence, which folded in 1963. He also taught at the Conservatoire de Paris, succeeding Jean Rivier and Darius Milhaud as professor of composition (1966-1970).

He died on 20 December 1974, leaving behind an uncompleted opera, Bogomilé.