After receiving his doctorate in 1965 Williams was employed at the University of Arizona until 1983. From 1985 to 1993 he served as director of the Cerro Tololo Inter-American Observatory in Chile, and from 1993 to 1998 he was director of STSci.
As the director of STScI, he decided to devote a substantial fraction of his director's discretionary time on the Hubble Space Telescope in 1995 to the study of distant galaxies. This historic project resulted in the Hubble Deep Field, a landmark image showing in remarkable detail the structure of galaxies in the early universe. For his leadership of this project, he was awarded the 1998 Beatrice M. Tinsley Prize, the NASA Distinguished Public Service Medal in 1999, and the 2016 Karl Schwarzschild Medal.
A member of the American Academy of Arts & Sciences, Williams research specialties cover nebulae, novae, and emission-line spectroscopy and analysis. He is an advocate for science education and has lectured internationally on the discoveries of the Hubble Space Telescope. In 1996, Williams made the controversial decision to offer the directors discretionary time on the Hubble Space Telescope to two competing teams using distant supernovae to determine the universes expansion rate accurately. The two teams independently found that the universes expansion was accelerating due to a previously unknown energy source. The leaders of the two teams were awarded the 2011 Nobel Prize in Physics for the discovery.
In 2015 Williams retired and was appointed emeritus professor of STScI.