Born in Merriman, Nebraska, Fitch was educated at McGill and Columbia universities and obtained his PhD from Columbia in 1954. He then joined the Princeton staff, being appointed professor of physics there in 1960.

Working with Leo James Rainwater, Fitch was the first to observe radiation from muonic atoms; i.e., from species in which a muon is orbiting a nucleus rather than an electron. This work indicated that the sizes of atomic nuclei were smaller than had been supposed. He went on to study kaons and in 1964 collaborated with James Cronin, James Christenson, and René Turley in an experiment that disproved CP conservation. In 1980 Fitch and Cronin shared the Nobel Prize for physics for this fundamental work.