Sowerby studied in Chicago and in Rome as the first American winner of the Prix de Rome. He taught composition and theory at the American Conservatory of Music in Chicago from 1925 to 1962 and was organist at St. James Church (now Cathedral) there from 1927 to 1962. He became director in 1962 of the College of Church Musicians in Washington, D.C., where he also was associated with the National Cathedral (Episcopal).

Sowerby combined a fine melodic talent with a use of modern harmonies. His Canticle of the Sun for chorus and orchestra (1944), based on Matthew Arnold (Arnold, Matthew)'s translation of a canticle by St. Francis, won the Pulitzer Prize in 1946. His orchestral works include tone poems, notably Prairie (1929), and four symphonies (1921, 1927, 1940, and 1947). He also wrote chamber music; concerti for piano, cello, and organ; numerous choral and organ works; and for bandleader Paul Whiteman (Whiteman, Paul)'s orchestra, two symphonic jazz pieces entitled Synconata (1924) and Monotony (1925).