Goodpaster entered the United States Military Academy at West Point in 1935, followed in 1939 by a commission as a second lieutenant in the Corps of Engineers after graduating second in his class of 456.

After serving in Panama, he returned to the U.S. in mid-1942, and in 1943, he attended a wartime course at the Command and General Staff School, Fort Leavenworth, Kansas.

"[8] In 1996, along with General Lee Butler and Rear Admiral Eugene Carroll, Goodpaster co-authored a statement for the Global Security Institute advocating the complete elimination of nuclear weapons due to their danger and lack of military utility.

He served on American Security Council and founded the Committee on the Present Danger, emphasizing the Soviet Union's military threat and a corresponding need for a strong defense for the United States.

He served as a trustee and a chairman of the George C. Marshall Foundation, which established the Andrew J. Goodpaster Award to honor, "American business leaders, politicians, military leaders and others who have served our nation in exemplary ways, who, like General Goodpaster, have exhibited great courage, selfless service, patriotism and leadership in their lives and careers.

For many years in retirement, Goodpaster was a trustee of St. Mary's College of Maryland, playing important roles in advancing the school to national prominence.