After graduating from Marion Military Institute in 1924, he entered the United States Military Academy and graduated in 1928, receiving his commission in the Infantry.
He served with as executive officer of the 1st Special Service Force from 1942 to 1944, including during their assault on Kiska in 1943. Following that assignment, he became commanding officer of the 143d Infantry Regiment, 36th Infantry Division, serving in the Mediterranean Theater (Operation Dragoon) and European Theater from January 1944 to January 1945. He served as Assistant Division Commander, 45th Infantry Division from January 1945 to January 1946.
This was followed by staff assignments to Headquarters, Army Ground Forces in 1946 and Command and General Staff College from 1947 to 1950.
He was a student and then faculty member at the Army War College from 1950 to 1951, before being deployed to fight in the Korean War. He consecutively served as Commanding General, 25th Infantry Division, Chief of Staff of X Corps, and Chief of Staff Eighth United States Army during the Korean War.
He later served as Commanding General, United States. Army Forces in the Middle East in 1958. From 1959 to 1960, he commanded V Corps.
After receiving his fourth star in 1961, he became Commander-in-Chief, United States Strike Command, from 1961 to 1966.
General Adams retired in 1966. He was president of Paul Doctorate. Adams & Associates from 1966 to 1971. He died on October 31, 1987 in Tampa, Florida.