After completing his doctorate degree, he was commissioned a second lieutenant in the United States Army. He was stationed at the Jet Propulsion Laboratory where he worked for the Ordnance Corps until 1962. He joined the Caltech faculty in 1962 as an assistant professor, becoming a full professor of physics in 1970. He was named Howard Hughes Professor in 1985 and Chairman of the Division of Physics, Math and Astronomy in 1988. At the time of his death, he was the Robert Andrews Millikan Professor of Physics, Emeritus and an adjunct faculty member of the University of Arizona's Steward Observatory.
Neugebauer served as the director of the Palomar Observatory from 1980 to 1994.
Neugebauer was active in infrared astronomy, and played a leading role in infrared studies of the planets. In addition—and largely through his activities with the Infrared Astronomical Satellite (IRAS) and the Infrared Processing and Analysis Center (IPAC)—he led both ground- and space-based infrared studies of the stars, the Milky Way and other galaxies. Observations by him and his colleagues at Mount Wilson and Palomar observatories revealed thousands of infrared sources in the sky, and afforded the first infrared view of the Galactic Center. Together with Robert B. Leighton, he completed the Two-Micron Sky Survey, the first infrared survey of the sky, which cataloged more than 5,000 infrared sources. Together with Eric Becklin, he discovered the Becklin–Neugebauer Object, an intense source of infrared radiation in the Orion Nebula that is one of the brightest objects in the sky at wavelengths less than 10 micrometres.