Henry was born on April 7, 1801, in New York City to his father, an immigrant from Dublin, who served in the Irish Brigade during the War of 1812.

[1] Eagle commanded the bomb vessel 2Etna and a division of the Pacific Squadron during the Mexican–American War and was then made a civil, military and trade governor of Tabasco.

[1] When the American Civil War broke out, Eagle was the bearer of communications between Manhattan and Brooklyn as well as volunteering to command the USS Monticello and took it into Norfolk, Virginia to blockade the Chesapeake Bay at the Battle of Sewell's Point.

He later commanded the USS Santee[2] and captured and destroyed the privateer Royal Yacht at the Battle of Galveston Harbor.

[1] This resulted in Eagle being promoted to Commodore in 1862 and on January 1, 1863, he was placed on the retired list as well as being a prize commissioner in 1864 and 1865.