Norrish was educated at the university in his native Cambridge. Apart from the war years, he spent his whole career there, serving as professor of physical chemistry from 1937 until 1965.

Norrish made his important contributions to chemistry in the fields of photochemistry and chemical kinetics, being introduced to these by Eric Rideal during his PhD work. From 1949 to 1965 he collaborated with his former pupil George Porter in the development of flash photolysis and kinetic spectroscopy for the investigation of very fast reactions. For their work they shared the 1967 Nobel Prize for chemistry with Manfred Eigen.

Norrish also made a significant contribution to chemistry when he showed the need to modify Draper's law. In the mid-19th century John Draper proposed his law that the amount of photochemical change is proportional to the intensity of the light multiplied by the time for which it acts. Norrish was able to show that the rate should be proportional to the square root of the light intensity.