He was educated at the University of Chicago, where he received bachelor's and master's degrees in physics and a PhD in astronomy in 1952. He was a student of Subrahmanyan Chandrasekhar while working at University of Chicago's Yerkes Observatory. His work there with William Wilson Morgan and Stewart Sharpless showed the existence of the Milky Way's spiral arms.
He became a post-doctoral researcher, instructor and Assistant Professor at the California Institute of Technology until 1958. He was then appointed Assistant Professor at the University of Wisconsin–Madison, received tenure there in 1959, and was promoted to full professor in 1961. He was a Guggenheim Fellow for the academic year 1960–1961. In 1973 he moved from Madison to the University of California at Santa Cruz, as Professor of Astronomy and Astrophysics, and Director of Lick Observatory, a position he held until 1981. He remained on the faculty at UC Santa Cruz until his retirement in 1993. Thereafter, Emeritus Professor Osterbrock continued to make daily trips to his office on campus, to work on his research, to keep publishing, and to maintain an active role in the astronomical community.
At the time of his death he had authored 12 monographs on astronomy and the history of astronomy, including, in 1989 the influential textbook Astrophysics of Gaseous Nebulae and Active Galactic Nuclei, and the recently updated and revised 2nd edition (2006) written along with Gary Ferland of the University of Kentucky. Alongside his more than 150 articles on astronomy and astrophysics, he published 70 historical studies, biographical memoirs, and obituaries of major figures in nineteenth and twentieth century astronomy, and numerous book reviews.
Osterbrock received lifetime achievement awards from the American Astronomical Society and the Astronomical Society of the Pacific. He was President of the American Astronomical Society from 1988 to 1990.
He died following a heart attack. He was survived by his wife of 54 years, Irene Hansen, and their son and two daughters.