Otto Neugebauer was born on May 26, 1899 in Innsbruck, Austria. His parents died when he was young and he was raised by an uncle. He attended Gymnasium in Graz, then served in the Austrian army upon graduation in 1917. During World War I he spent a year in an Italian prisoner-of-war camp, where he met Ludwig Wittgenstein. From 1919 to 1921 he studied electrical engineering and physics at the University of Graz. He transferred to the University of Munich in 1921, where he studied with physicist Arnold Sommerfeld and mathematician Arthur Rosenthal. He then moved to the University of Göttingen, where he assisted mathematician Richard Courant and supervised the university's mathematical reading room. (Neugebauer later designed Göttingen's new mathematical institute, built in 1929.) He completed his Ph.D. on Egpytian fractions in 1926, and received his venia legendi in 1927. He also received an Ll.D. from St. Andrews University in Scotland in 1938.

He remained at Göttingen, was appointed an associate professor in 1932, and named acting director of the mathematical institute in 1933, in the wake of the firing of the Jewish mathematican Courant by the Nazi regime. Neugebauer himself was later fired after refusing to take the Nazi loyalty oath. Harald Bohr arranged for Neugebauer to become a professor at the University of Copenhagen, where he remained until 1939. Neugebauer was then brought to Brown University in the United States to edit a new journal titled "Mathematical Reviews". "Mathematical Reviews" was modeled on the influential"Zentralblatt für Mathematik und ihre Grenzgebiete," which Neugebauer had founded in 1931 and edited until the influence of Nazi policies on the editorial process caused him to resign in protest in 1938. He continued with the new journal until 1948.

In 1945 he and his collaborator Abraham Sachs were invited by Hermann Weyl to spend the year as members of the School of Mathematics at the Institute for Advanced Study. This was the beginning of Neugebauer's long association with the Institute. He returned as a member for the second semester of the 1949-1950 academic year, then was offered a five-year membership beginning with the 1950-1951 year. Duties at Brown prevented him from accepting fully, but he made arrangements to be at the Institute "for one term every second year." In later years, he was in residence a great deal more often than the original agreement. While he retired from Brown in 1969, he held a permanent appointment at the Institute from 1980 until his death in 1990. Unusually, he was active in four schools (the School of Mathematics, the School of Humanistic Studies, the School of Historical Studies, and the School of Natural Sciences) during his long affiliation with the Institute.

Neugebauer was a prolific writer, and published on a range of topics, including Babylonian mathematics, mediaeval astronomy, and chronology. Among his books were the three-volume "A History of Ancient Mathematical Astronomy" (1975), the three-volume "Astronomical Cuneiform Texts" (1955), and "The Exact Sciences in Antiquity" (1951, with a second edition in 1957). Near the end of his career his notes on Copernicus' "De Revolutionibus" were published in collaboration with Noel Swerdlow. He received many awards and honors, including the Balzan Prize (1986) and the Franklin Medal of the American Philosophical Society (1987), and was a member of the National Academy of Sciences and the Académie des Inscriptions et Belles-Lettres, among other international affiliations.

He married Grete Bruck, a fellow mathematics student, in 1927. They had two children: a daughter, Margo, and a son, Gerald. Neugebauer died on February 19, 1990.