The son of Russian-Jewish immigrants, Rabinowitz studied chemistry for one year at New York University before embarking on a career as a dancer in 1936. He studied a wide array of dance traditions, appeared with the Gluck Sandor–Felicia Sorel Dance Center, and danced in the chorus of several Broadway musicals. In 1940 he joined the Ballet Theater (now the American Ballet Theatre), where he soon began dancing such important roles as Petrouchka. (About this time he and his parents changed the family name to Robbins.) In 1944 Robbins choreographed his first, spectacularly successful ballet, Fancy Free, with a musical score by the young composer Leonard Bernstein (Bernstein, Leonard). This ballet, featuring three American sailors on shore leave in New York City during World War II, displayed Robbins' acute sense of theatre and his ability to capture the essence of contemporary American dance using the vocabulary of classical ballet. Later that year Robbins and Bernstein, in collaboration with the lyricists Betty Comden and Adolf Green, expanded Fancy Free into a successful Broadway musical called On the Town.

For the next phase of his career Robbins was to divide his time between musicals and ballet. He created such ballets as Interplay (1945) and Facsimile (1946). In 1948 Robbins joined the newly founded New York City Ballet (NYCB) as both dancer and choreographer, and the following year he became its associate artistic director under George Balanchine (Balanchine, George). Robbins created many important ballets for NYCB, some of the earliest being The Cage (1951), Afternoon of a Faun (1953), and The Concert (1956). These innovative works display his gift for capturing the essence of a particular era through his mastery of vernacular dance styles and his understanding of gesture.

For the Broadway stage, Robbins choreographed a string of musicals, including Billion Dollar Baby (1946), High Button Shoes (1947), and Look Ma, I'm Dancin' (1948). Robbins won the Antoinette Perry (Tony) Award for best choreographer in 1948 for High Button Shoes. He also created the dance sequences for the musicals Call Me Madam (1950), Rodgers and Hammerstein's The King and I (1951), and The Pajama Game (1954); and he adapted, choreographed, and directed a musical version of Peter Pan (1954) that was subsequently adapted for television in 1955 and for which Robbins won an Emmy Award.

His Broadway career is well represented by West Side Story (1957), a musical that transplants the tragic story of Romeo and Juliet to the gritty milieu of rival street gangs in New York City. Robbins conceived, directed, and choreographed this work, which featured a musical score by Bernstein, lyrics by Stephen Sondheim (Sondheim, Stephen), and set designs by Robbins' longtime collaborator Oliver Smith. West Side Story was immediately recognized as a major achievement in the history of the American musical theatre, with its innovative setting, electric pacing, and tense, volatile dance sequences. Robbins received the 1958 Tony Award for best choreography for the Broadway version and Academy Awards for his choreography and codirection (with Robert Wise) of the highly successful 1961 film version. (The original musical was successfully revived on Broadway in 1980.) He directed and choreographed the popular musical Gypsy in 1959 and the even more successful Fiddler on the Roof in 1964.

It was after Fiddler on the Roof that Robbins turned his attention more exclusively to the ballet. Since 1958 Robbins had worked with the ballet company he had founded, Ballets U.S.A., which toured sporadically until 1961. In 1965 Robbins resumed creating ballets with his acclaimed Les Noces. For the next three years he worked on an experimental theatre project, the American Theatre Laboratory, but in 1969 he returned to NYCB. He was a resident choreographer and a ballet master there until 1983, when he and Peter Martins became ballet masters in chief (codirectors) of the company shortly before Balanchine's death. Robbins continued to write ballets for NYCB, including Dances at a Gathering (1969); The Goldberg Variations (1971); Requiem Canticles (1972); In G Major (1975); Glass Pieces, performed to the music of Phillip Glass (1983); In Memory of... (1985); Ives, Songs (1988); and West Side Story Suite (1995). Many of his later ballets are more classical in style and more abstract in subject matter than his earlier works.

Jerome Robbins' Broadway, a compilation of excerpts from 11 Broadway musicals that Robbins had directed or choreographed, opened on Broadway in 1989. Robbins resigned as codirector of NYCB in 1990, though he continued to choreograph for the company. His last work, Brandenburg, premiered there in 1997.