Smoot was born in Yukon, Florida. He graduated from Upper Arlington High School in Upper Arlington, Ohio, in 1962. He studied mathematics before switching to the Massachusetts Institute of Technology where he obtained dual bachelor's degrees in mathematics and physics in 1966 and a Ph.D. in particle physics in 1970.
Although Smoot attended MIT, he is not the Smoot who was laid end to end to measure the Harvard Bridge between Cambridge and Boston, creating the humorous Smoot unit of measure in the process. This was in fact his cousin Oliver R. Smoot, an MIT alumnus who later served as the chairman of the American National Standards Institute.