Martell was born in Spencer, Massachusetts. He attended the U.S. Military Academy in West Point, New York. He was commissioned as a second lieutenant after graduating in 1942 and served in the Okinawa campaign of World War II, retiring with the rank of lieutenant colonel. He received a Ph.D. in radiochemistry from the University of Chicago in 1950. Willard Libby was Martell's mentor at the university through the late 1940s and early 1950s.