Donovan studied at Yale University from 1912 to 1914, then at the Institute of Musical Arts in New York until 1918. In Paris he was a student of Charles-Marie Widor. From 1920 to 1923 he taught at Taft School in Watertown and from 1923 to 1928 at Smith College in Northampton. From 1928 he was a member of the music faculty of Yale University. In 1940 he succeeded David Stanley Smith as dean of the faculty and from 1954 until his retirement in 1960 he held a professorship. He also taught at the Institute of Musical Arts (1925-1928) and at Finch College in New York (1926-1940).
From 1928 to 1965 Donovan was organist at Christ Church in New Heaven. He was also conductor of the Bach Cantata Club (from 1933 to 1944) and the New Heaven Symphony Orchestra (from 1936 to 1951) and conducted the New York Symphony Orchestra in the 1936-1937 season. He was instrumental in organizing the Yaddo Music Festival in Saratoga Springs. 1961-1962 he was president of the American Composers' Alliance.
As a composer, Donovan has performed chamber music, vocal and orchestral works, including two symphonies, the overture New England Cronicle, the symphonic poem Smoke and Steel, songs, a mass and a Magnificat.