He is best known as the Lieutenant Colonel in command of the 1st Battalion, 7th Cavalry Regiment, at the Battle of Ia Drang, in 1965 during the Vietnam War; today, he is the "honorary colonel" of the Regiment.

Born in Bardstown, Kentucky, Moore's chances of obtaining an appointment to West Point were reduced due to the demographics of the area. Moore therefore moved to Washington, D.C., where he completed his high school education, and attended George Washington University for two years before receiving his appointment from a Georgia congressman in 1942 (despite having never before been to Georgia). He graduated from West Point in 1945 and attended graduate studies at George Washington and Harvard universities, obtaining a master's degree in international relations from the latter.

Moore was commissioned as a second lieutenant in 1945. He served with the 187th Airborne Infantry Regiment in Japan from 1945 until 1948. In 1948 he was re-assigned to Fort Bragg. While with the 82nd Airborne Division, he volunteered to join the Airborne Test Section, a special unit testing experimental parachutes, and he made some 150 jumps with the Section over the next two years.

In 1952 Moore was assigned to the 17th Infantry Regiment of the 7th Infantry Division as a Captain in Korean War. While in Korea, he commanded both a rifle company and a heavy mortar company in combat. He next served as Regimental and then Divisional Assistant Chief-of-Staff, Operations and Plans.

In 1954, Moore returned to West Point, this time as a Major, and served for three years as an instructor in infantry tactics. While serving as an instructor at West Point, Moore taught then-Cadet Norman Schwarzkopf, who called Moore one of his "heroes," and cites Moore as the reason he chose the infantry branch upon graduation. Schwarzkopf later became a general and led the UN Coalition forces in the 1991 Gulf War against Iraq.

Moore next attended the Command and General Staff College, followed by a three-year tour in the Office, Chief of Research and Development where his initiative and insights were key to the development of new airborne equipment and airborne/air assault tactics. Following graduation from the Armed Forces Staff College in 1960 Moore served a three-year tour with Headquarters, Allied Forces Northern Europe in Oslo, Norway.

In 1964, Lieutenant Colonel Moore completed the course of study at the National War College, while earning a master's degree in International Affairs from George Washington University. Moore was transferred to Fort Benning and commanded a battalion in the 11th Air Assault Division, undergoing air assault and air mobility training and tests until July 1965, when the Division was redesignated the 1st Cavalry Division.

Lieutenant Colonel Moore then took his battalion, the 1st battalion, 7th U.S. Cavalry (then in the 3rd Brigade Combat Team, 1st Cavalry Division) to South Vietnam, and to the famous Battle of Ia Drang. Encircled by enemy soldiers with no clear landing zone (LZ) that would allow them to leave, Moore managed to persevere despite overwhelming odds that led to a sister battalion only two-and-a-half miles away being massacred. Moore's dictum that "there is always one more thing you can do to increase your odds of success" and the courage of his entire command are credited with this astounding outcome. Importantly, despite the fact that Moore's spirited defense led to more than a 4-to-1 ratio between North Vietnamese casualties and U.S. casualties in their first major engagement of the war, Moore considers the battle a draw because the U.S. left the area and allowed the North Vietnamese to reassert control. Many consider this early battle a microcosm of the later war. Moore was known as "Yellow Hair" to his troops at the battle at Ia Drang, for his blonde hair, and as a tongue-in-cheek homage referencing George Armstrong Custer, commander of the same unit (7th Cavalry) at the Battle of the Little Bighorn just under a century before.

After Vietnam, Moore served as Assistant Chief-of-Staff, Operations and Plans of the Eight Army in South Korea, and Commanding General of the 7th Infantry Division, before rotating back stateside. As Commanding General of the Army Training Center at Fort Ord, California in 1971-1973, he oversaw extensive experimentation in adapting basic and advanced individual training under Project VOLAR in preparation for the end of conscription and the institution of the Modern Volunteer Army. His final assignments took him to the East Coast, as Commanding General of the Military Personnel Center, and finally, Deputy Chief of Staff for Personnel, Department of the Army.

After his retirement in 1977, Moore served as the Executive President of the Crested Butte Ski Area, Colorado. In June 2009, the 87-year-old Moore attended the formal opening of the National Infantry Museum in Columbus, Georgia. One of the featured exhibits of the museum is a life-size diorama of LZ X-Ray from the Battle of Ia Drang. In 2010 Moore was a signatory to the "1000+ Flag & General Officers Affirm Law on Gays," which opposes proposed changes in rules concerning gays serving in the US military.