Snell was born in Bradford, Massachusetts, and educated at Dartmouth and Harvard, where he obtained his doctorate in 1930. After brief appointments at Texas, Brown, and Washington University, St. Louis, he joined the staff of the Jackson Laboratory, Bar Harbor, Maine, in 1935 and remained there for his entire career, retiring finally in 1969.

Early in his career, while at the University of Texas, Snell was the first to show that x-rays can cause mutations in mammals, by his demonstration that x-rays induce chromosome translocations in mice. His main work concerned what he called the major histocompatibility complex. It had been known since the 1920s that although skin grafts between mice are generally rapidly rejected they survive best when made between the same inbred line. Snell's coworker Peter Gorer showed in 1937 that this was due to the presence of certain histocompatibility antigens found on the surface of mouse cells and since known as the H-2 antigens. In the 1940s Snell began a detailed study of the system.

His first task was to develop inbred strains of mice through backcrossing, genetically identical except at the H-2 locus. After much effort he was able to show that the H-2 antigens were controlled by the genes at the H-2 complex of chromosome 17, described by him as the major histocompatibility complex (MHC).

It was for this work that Snell shared the 1980 Nobel Prize for physiology or medicine with Jean Dausset and Baruj Benacerraf.