After completing his doctorate degree, he was commissioned a second lieutenant in the United States Army.
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 played a role in the design and construction of the W. M. Keck Observatory in Hawaii.
Among Neugebauer's numerous awards are two NASA Exceptional Scientific Achievement Medals (1972, 1984), the 1985 Space Science Award of the American Institute of Aeronautics and Astronautics, the 1985 Richmyer Lecture Award, the 1986 Rumford Prize, the 1996 Henry Norris Russell Lectureship, the 1998 Herschel Medal, and the 2010 Bruce Medal.