Although born in Blankenburg, Germany, Kusch spent all but the first year of his life as a resident of the United States, becoming a naturalized citizen in 1922. His early education was in the Midwest of the United States, and his undergraduate studies were at the Case Institute of Technology, Cleveland, Ohio. Starting in chemistry, he made an early switch to physics, and gained his BS in 1931. He followed this with work as a research assistant at the University of Illinois on problems of optical molecular spectroscopy, gaining his MS there in 1933 and his PhD in 1936. This was followed by a short period at the University of Minnesota researching mass spectroscopy (1936–37). From 1937 to 1972 he was associated with the physics department of Columbia University, New York City, apart from interruptions in World War II when, he was engaged in research on the military applications of vacuum tubes and microwave generators at Westinghouse Electric Corporation (1941–42) and Bell Telephone Laboratories (1944–46).

At Columbia, Kusch began work under Isidor Rabi on the first radiofrequency spectroscopy experiments using atomic and molecular beams. His research was principally on the fine details of the interactions of the constituent particles of atoms and molecules with each other and with an externally applied magnetic field. In particular, Kusch made accurate determinations of the magnetic moment of the electron as deduced from the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance to theories of the interactions of electrons and electromagnetic radiation (now known as quantum electrodynamics). It was for his precise work in measuring the electron's magnetic moment that he received the 1955 Nobel Prize for physics, sharing it with Willis Lamb, who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.

Kusch's career at Columbia University took him to associate professorship (1946), professorship (1949), and executive director of the Columbia Radiation Laboratory (1952–60), vice president and dean of the faculty (1969–70), and executive vice president and provost (1970–71). In 1972 he left to become professor of physics, and then Eugene McDermott Professor, at the University of Texas at Dallas. EX