Kusch received his bachelor's degree in physics in 1931 from Case Western Reserve University. From the University of Illinois, he received his master's degree in 1933 and his Ph.D. in 1936. He spent much of his career as a professor at Columbia University in New York City, and served as the university's provost for several years before departing for the newly created University of Texas at Dallas. He worked on molecular beam resonance studies under I. I. Rabi, then discovered the electron anomalous magnet moment. Many measurements of magnetic moments and hyperfine structure followed. He expanded into chemical physics and continued to publish research on molecular beams. During his tenure at Columbia, he was the doctoral supervisor for Gordon Gould, the Inventor of the laser.
Kusch House, a residential dormitory for undergraduate students at Case Western Reserve University in Cleveland, Ohio on the South Campus is named after Kusch. It is located on Carlton Road in Cleveland Heights. His widow Betty died in 2003, aged 77.