Hoyle graduated from the United States Military Academy at West Point in 1875, and was commissioned as a second lieutenant of Field Artillery.

His brother George S. Hoyle and he were notable as two of the first post-American Civil War West Point students from former Confederate states.

During his World War I recall to active duty he was assigned as commander of the Department of the East, with primary responsibility for the Governor's Island Port of Embarkation in New York Harbor.

The citation for the medal reads: The President of the United States of America, authorized by Act of Congress, July 9, 1918, takes pride in presenting the Army Distinguished Service Medal (Posthumously) to Brigadier General Eli D. Hoyle, United States Army, for exceptionally meritorious and distinguished services to the Government of the United States, in a duty of great responsibility during World War I.

Their son Rene Edward De Russy Hoyle (1883–1981) was a career Army officer who attained the rank of major general.