Reeve graduated from the United States Military Academy in July 1835, and was initially assigned to the 4th Infantry.
He received the brevet of major in August 1847 and lieutenant colonel in September 1847 for gallant and meritorious service at Contreras, Churubusco, and Molino del Rey.
Reeve commanded the expedition against the Pinal Apaches 1858–1859, but was made prisoner of war near San Antonio, Texas by Gen. David E. Twiggs on 9 May 1861.
Reeve was chief mustering and disbursing officer in New York City, 1862–1863, became lieutenant colonel in September 1862, and was in command of the draft rendezvous at Pittsburgh, Pennsylvania, 1864–1865.
He became colonel of the 13th Infantry in October 1864, and was brevetted brigadier general in the U.S. Army, 13 March 1865, "for faithful and meritorious service during the civil war.