Hageman was born and raised in Leeuwarden, Friesland, Netherlands. He was the son of Maurits Hageman of Zutphen and Hester Westerhoven of Amsterdam. A child prodigy, he was a concert pianist by the age of six. He studied in Amsterdam and gave lessons as a piano teacher. As a young man he was an accompanist for singers and with the Amsterdam Royal Opera Company, of which he became the conductor in 1899. For a short time he was accompanist to Mathilde Marchesi in Paris. He travelled to the United States in 1906 to accompany Yvette Guilbert on a national tour. He stayed and eventually became an American citizen.

He was a conductor for the Metropolitan Opera between 1914 and 1932, head of the opera department at the Curtis Institute from 1932 to 1936, and music director of the Chicago Civic Opera and the Ravinia Park Opera for seven years. He was a guest director of orchestras like the Chicago, Philadelphia, and Los Angeles symphony orchestras. He conducted the Philadelphia Orchestra summer concerts for four years and from 1938 on he conducted at the Hollywood Bowl summer concerts for six seasons.

He is known to the film community for his work as an actor and film score composer, most notably for his work on several John Ford films in the late 1930s. He shared an Academy Award for his score to Ford’s 1939 western Stagecoach. He also had minor roles in eleven movies, for example as opera conductor in The Great Caruso. He became a member of ASCAP in 1950.

Hageman also composed more serious vocal music. His 1931 opera Caponsacchi, first performed in Freiburg with the title Tragödie in Arezzo in 1932, was staged at the Metropolitan Opera in 1937 with Lawrence Tibbett in the title role. His "concert drama" The Crucible was performed in Los Angeles in 1943. While his large musical compositions are rarely heard today, a few of his art songs are well known and highly regarded, especially "Do Not Go, My Love", a setting of a Rabindranath Tagore poem.

He was a National Patron of Delta Omicron, an international professional music fraternity.