Henry Morse was born in Charlottesville, Virginia, around 1837, and he enlisted in the Union army on February 27, 1864, near Clarksville, Tennessee. Morse worked as a farmer before the war, although it is unclear whether or not he was enslaved at the time of his enlistment. His service records describe him as 5 feet, 7 inches tall, with black hair, brown eyes, and a brown skin complexion. Morse enlisted for a period of three years, and he mustered in as a private in Company F of the 16th USCT Infantry Regiment near Clarksville on March 9.  

During the war, the 16th USCT served throughout Tennessee. The regiment helped repel Confederate General John Bell Hood's advance at the Battle of Nashville, and it pursued Hood's Army of Tennessee into northern Alabama. Afterward, the 16th USCT mostly moved around central and eastern Tennessee, performing garrison duty in a number of towns and cities. Morse died of smallpox on April 5, 1865, at the smallpox hospital near Chattanooga, only twenty days before his regiment mustered out and returned home. No pension was ever field after his death.