Békésy, the son of a diplomat in the Hungarian capital, Budapest, studied chemistry at the University of Bern and physics at Budapest University, where he obtained his PhD in 1923. He immediately joined the research staff of the Hungarian Telephone Laboratory where he remained until 1946 while simultaneously holding the chair of experimental physics at Budapest University from 1939. He left Hungary in 1947, via the Swedish Karolinska Institute, for America, where he served first as a senior fellow in psychophysics at Harvard from 1949 to 1966 and finally as professor of sensory science at the University of Hawaii from 1966 until his death.

Békésy first worked on problems of long-distance telephone communication before moving to the study of the physical mechanisms of the cochlea within the inner ear. When he began this study it was generally thought, following the work of Hermann von Helmholtz, that sound waves entering the ear selectively stimulated a particular fiber of the basilar membrane; this in turn stimulated hairs of the organ of Corti resting on it, which transferred the signal to the auditory nerve.

Using the techniques of microsurgery, Békésy was able to show that a different mechanism is involved. He found that when sound enters the cochlea, a traveling wave sweeps along the basilar membrane. The wave amplitude increases to a maximum, falling sharply thereafter; it is this maximum point to which the organ of Corti is sensitive. For this insight into the mechanism of hearing, Békésy was awarded the 1961 Nobel Prize for physiology or medicine.