He was born in Auburndale, Massachusetts. After early study in the United States with George Whitefield Chadwick and others, he went to Europe, a common destination for a young American composer in the 1880s. In Munich he studied with Josef Rheinberger; also in Munich he composed his first significant works, including a symphony and a dramatic cantata. After returning to the U.S. he took a succession of jobs as a teacher, organist and choirmaster, mostly in New York City. In 1893 he became professor at Yale University, a position which he held for the rest of his life. Parker died in Cedarhurst, New York.
While Parker is mostly remembered for a single work, the oratorio Hora novissima, based on the poem by Bernard of Cluny, he was a prolific and versatile composer in a mostly conservative Germanic tradition, writing two operas, songs, organ music, incidental music, and a copious quantity of music for chorus and orchestra. Influences in his music include Mendelssohn, Brahms, Wagner, as well as Debussy and Elgar in some works which he composed closer to 1900. During his lifetime he was considered to be the finest composer in the United States, a superior craftsman writing in the most advanced style.
In 1892, Parker composed the hymn tune "Auburndale" in celebration of the laying of the cornerstone of the new church building of the Episcopal parish he was baptised in, Parish of the Messiah His father, Charles Parker, had been the architect for that congregation's chapel; famed Episcopal bishop Phillips Brooks laid the cornerstone. "Auburndale" was later published in the 1918 Hymnal ("The Messiah Miracle: A History The Church of the Messiah of West Newton and Auburndale 1871-1971," privately published, 1971).
Parker entered his opera, Mona, into a contest at the Metropolitan Opera winning the prize for best composition in 1911. He won 10,000 dollars and his opera was performed by the company. Mona premiered on March 14, 1912 and ran for four performances. The title role was created by Louise Homer.