Kohn was born in Vienna. From 1950 to 1960, he was professor at the Carnegie Institute of Technology in Pittsburgh, USA. He then joined the University of California in San Diego, remaining there until 1979 when he became director of the Institute of Theoretical Physics in Santa Barbara. He gave up that appointment in 1984, although he was active at the Institute for many years. In 1998 Kohn shared the Nobel Prize for chemistry with John Pople. Kohn received his award for his development of density-functional theory in quantum chemistry, for which he used powerful computer techniques.

Quantum chemistry – the solving of chemical problems using quantum mechanics – began to expand in the 1960s when computers became available to do the calculations. Kohn had already shown in 1964 that, for a system described by quantum mechanics, the total energy can be calculated if the electron density (distribution of electrons) is known. His later work concerned the simplification of the mathematics needed to describe the bonding in atoms and in mapping chemical reactions. He demonstrated that it is not necessary to be able to describe the motion of each individual electron in a molecule; it is sufficient to know the average number of electrons located at a particular point in space. The resulting density-functional theory is simpler to analyze using a computer, and can be employed for very large biologically important molecules.