Wigner studied chemical engineering and received his Ph.D. from the Institute of Technology in Berlin in 1925. After serving as a lecturer there and at the University of Göttingen, he went to the United States. Apart from two years (1936–38) as professor of physics at the University of Wisconsin, he spent his academic life at Princeton University, serving as a professor of mathematical physics from 1938 until his retirement in 1971. He became a naturalized U.S. citizen in 1937.

At Göttingen, Wigner formulated his law of the conservation of parity, which implies that it is impossible to distinguish left from right in fundamental physical interactions. This theory became an integral part of quantum mechanics, but in 1956 the physicists Tsung-Dao Lee and Chen Ning Yang showed that parity is not always conserved in weak interactions of subatomic particles. At Princeton, Wigner determined that the nuclear force that binds neutrons and protons together is necessarily short-range and independent of any electric charge. He also developed the principles involved in applying mathematical group theory to investigate the energy levels of atomic nuclei. In 1936 he worked out the theory of neutron absorption (neutron capture), which later proved useful in building nuclear reactors.

In 1939, Wigner helped Leo Szilard persuade Albert Einstein (Einstein, Albert) to write the historic letter to President Franklin D. Roosevelt that set in motion the U.S. atomic-bomb project. During World War II he worked at the Metallurgical Laboratory at the University of Chicago, where he helped Enrico Fermi (Fermi, Enrico) construct the first atomic pile. Wigner also conducted research on quantum mechanics, the theory of the rates of chemical reactions, and nuclear structure. His publications include Gruppentheorie und Ihre Anwendung auf die Quantenmechanik der Atomspektren (1931; Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra), a classic text, and Symmetries and Reflections (1967).