He graduated from the United States Military Academy in 1930 and was commissioned in the field artillery.
He began his career in the horse artillery with the 4th Field Artillery from 1931 to 1934. Other early assignments included teaching physics at West Point and various staff assignments. O'Meara served as a battery commander in the 4th Armored Division in 1941, and in 1942 took command of the 94th Field Artillery Battalion.
By the end of World War II he was the Assistant Artillery Commander of VII Corps. Following the war, he attended the Command and General Staff College in 1946, and the National War College from 1951 to 1952. During the Korean War he was the artillery commander for the 7th Infantry Division, and later the artillery commander for IX Corps.
Promoted to Brigadier General in 1952, he earned the in 1953 for reconnaissance near Kumhwa. He spent the years after Korea working in research and development for the army, first with the Research & Development Division of the Army General Staff, then as Deputy Chief of Research & Development for the U.S.Army from 1955 to 1957. He then took command of the 4th Armored Division in 1957.
From 1959 to 1961, he was assigned to France as director of military assistance for the United States European Command followed by command of the United States Southern Command and U.S. Army Europe. O'Meara was an avid squash player, and during his tenure at both SOUTHCOM and U.S. Army Europe ordered the installation of squash courts at bases under his command. O'Meara retired from the Army in 1967, settling in the Washington, D.C. area.
He died on September 30, 2005 of a stroke at the age of 98 in Arlington, Virginia and was buried in Arlington National Cemetery.