Tompkins was born in Fort Monroe, Virginia on September 12, 1830. He was the son of Colonel Daniel D. Tompkins, a career Army officer, and was the grand nephew of Vice President Daniel D. Tompkins. He received an appointment to West Point from Brooklyn, New York as a member of the class of 1851, though he did not graduate with his class. He resigned in 1849 for unspecified reasons. Tompkins pursued private business interests until enlisting as a Private in the First Dragoons in January 1856, rising to the rank of sergeant before his enlistment ended in January 1861. He served on the western frontier and was recognized for his performance at the Second Battle of Pyramid Lake near Pyramid Lake, Nevada in June 1860. Tompkins received his commission as a 2nd lieutenant in the 2nd U.S. Cavalry Regiment in March 1861. It was in this unit that he gained fame for his heroism in action at the Battle of Fairfax Court House while a 1st lieutenant, to which he was promoted on April 30, 1861. Tompkins was reassigned to the 5th U.S. Cavalry Regiment on August 3, 1861 and served as the regimental quartermaster. On April 24, 1862 he received a volunteer commission as colonel of the 1st Vermont Cavalry. He resigned his volunteer commission on September 9, 1862. During the war, he received brevets to major, lieutenant colonel, colonel and brigadier general.
Medal of Honor citation
"Twice charged through the enemy's lines and, taking a carbine from an enlisted man, shot the enemy's captain." Captain John Quincy Marr was the first Confederate soldier killed in combat during the Civil War.
Postbellum
Tompkins was appointed as one of the nine officers assigned to the military commission investigating the conspirators involved in President Lincoln's assassination. Because of a dispute with General Grant, between 1866 and 1881 he was posted to numerous remote and austere western posts. He served the remainder of his career in the Quartermaster Corps, rising to Assistant Quartermaster General on January 24, 1881. The position of Assistant Quartermaster General, carried a rank of colonel in the Regular Army, to which Tompkins was promoted the same day. He finished his career serving on the east coast, voluntarily retiring on September 12, 1894. Tompkins suffered a broken leg in September 1914 and the wound never healed properly. He died of sepsis in Washington, D.C. on January 18, 1915. He is buried at Oak Hill Cemetery in Washington, DC.