Moore began writing popular songs at an early age, collaborating with classmate playwright Archibald MacLeish, and at Yale wrote tunes such as "Goodnight Harvard" and "Naomi, my Restaurant Queen," while undertaking composition studies with Horatio Parker. He graduated in 1917, served in the Navy until 1919, and continued writing pop tunes with John Jacob Niles, later collected as Songs My Mother Never Taught Me.
In Paris, Moore's studies with Vincent d'Indy influenced his harmonic style. In 1921, he joined the Cleveland Museum, organizing a concert series and playing the organ, and studied with Ernest Bloch.
He began writing for orchestra such works as Four Museum Pieces (1923) and The Pageant of P.T. Barnum (1924), a picturesque and tuneful set of five portraits describing events and people in the life of the (in)famous showman. In 1926, Moore became a teacher at Barnard College at Columbia University, then in 1940 was made head of the music department, where he remained until retiring in 1962.
His works include incidental music for Shakespeare's Twelfth Nights and Much Ado about Nothing, chamber music, and orchestral works. In 1935, Moore wrote his first of ten operas, White Wings. The operas are notable for their fine musical characterizations, clear vocal lines, and excellent sense of timing. There immediately followed The Headless Horseman (1936) and The Devil and Daniel Webster (1938), which is a staple of the American opera repertory. Moore then scored three films in the 1940s, as well as writing in other genres, then wrote Giants in the Earth, for which he won the Pulitzer Prize in 1951. Moore's popular opera The Ballad of Baby Doe (1956) is written in a vivid and forthright American style. His last operas all have remarkable orchestrations.
Moore was the founder of many composers' organizations, and president of both the National Institute and the American Academy of Arts and Letters. He received five honorary degrees and a Guggenheim Fellowship.