He shared a Nobel Prize in Chemistry in 1972, with Christian B. Anfinsen and William Howard Stein, for work done at Rockefeller University on the structure of the enzyme ribonuclease and for contributing to the understanding of the connection between the chemical structure and catalytic activity of the ribonuclease molecule.

Moore attended Peabody Demonstration School, now known as University School of Nashville, and in 1935 graduated summa cum laude from Vanderbilt University, where he was a member of Phi Kappa Sigma.

Moore then joined the staff of the Rockefeller Institute, later Rockefeller University, where he spent his entire professional career, with the exception of a period of government service during World War II.

In 1958, he and William H. Stein developed the first automated amino acid analyzer, which facilitated the determination of protein sequences.

In 1959, Moore and Stein announced the first determination of the complete amino acid sequence of an enzyme, ribonuclease, work which was cited in the Nobel award.