Damrosch studied with his father, Leopold Damrosch (1832–85), German violinist and conductor, who settled in New York City in 1871. Upon his father's death in 1885, Walter Damrosch assumed the conductorship of the New York Symphony Society and the Oratorio Society of New York, founded by his father, and also conducted at the Metropolitan Opera Company (from 1885 to 1891). In 1898 his brother Frank Damrosch (1853–1937) took over as conductor of the Oratorio Society of New York. Later, Walter Damrosch organized the Damrosch Opera Company (1894–1900), specializing in German operas. In 1903 he reorganized the New York Symphony Society and conducted it until 1927, when it was combined with the Philharmonic Society.

Like his father, Damrosch was an avowed propagandist of the Romantic composer Richard Wagner (Wagner, Richard); as early as March 3, 1886, he gave a concert performance of the opera Parsifal (first performed 1862) in New York. He also presented first American performances of symphonies by Johannes Brahms (Brahms, Johannes) and Pyotr Ilyich Tchaikovsky (Tchaikovsky, Pyotr Ilyich). Although not in sympathy with new music, he introduced several works by contemporary European and American composers. He was a pioneer of symphonic broadcasting and also established a weekly series of radio lectures on music appreciation for schools, which aired from 1928 to 1942.

A competent composer, Damrosch wrote several operas that were performed in New York, Boston, and Philadelphia, including The Scarlet Letter (1896), Cyrano de Bergerac (1913), The Man Without a Country (1937), and The Opera Cloak (1942). He also composed incidental music to plays and published an autobiography, My Musical Life (1923; 2nd ed., 1930).

Walter Damrosch's brother Frank was a founder and dean of the Juilliard School of Music.