He studied piano, music theory, and music criticism in New York and Boston, and it was in those two cities that he made his career as a music critic—first with the Boston Post (1906–1924) and then with the New York Times (1924–1955). He was also famous in radio broadcasting for his contributions to an intermission feature during the Metropolitan Opera Broadcasts, "The Metropolitan Opera Quiz." Occasionally, he appeared as a guest lecturer at universities and music conservatories.
While conservative in many regards, he was a champion of some new music in the first half of the 20th century. In particular, he often promoted the works of Prokofiev, Shostakovich, Stravinsky, and Hovhaness before they achieved worldwide fame.
By far his favorite living composer was Jean Sibelius, whom he championed throughout his career. Downes exchanged letters with the composer, and wrote a biography. Late in Sibelius's life, Finland awarded Downes honors and invited him to Finland to speak in honor of Sibelius's 75th birthday. According to some sources, the music of Sibelius became part of the standard orchestral repertory in the United States largely because of the championship of Downes. He is the father of music educator and radio host Edward Downes (quizmaster).
He died in New York. He was an honorary member of Phi Mu Alpha Sinfonia, the national fraternity for men in music.