Born in Iowa City, Sandage graduated from the University of Illinois in 1948 and obtained his PhD in 1953 from the California Institute of Technology. He was on the staff of the Hale Observatories at Mount Wilson and Mount Palomar from 1952 when he began as an assistant to Edwin Hubble. He was professor of physics at Johns Hopkins University (1987–88) and was on the staff of the Carnegie Observatories, Pasadena (1952–97), where he still worked until 2010.

In 1960, using the 200-inch (5-m) reflecting telescope, Sandage in collaboration with Thomas Matthews succeeded in making the first optical identification of a quasar or quasi-stellar object. Quasars first came to the notice of astronomers when a number of compact, rather than extended, radio sources were detected by the Cambridge surveys of the radio sky carried out in the 1950s. Sandage and Matthews showed that 3C 48, a compact radio source discovered during the third Cambridge survey, was at the same position as a faint apparently starlike object. Sandage and others succeeded in obtaining spectra of 3C 48 that were found to be quite unlike those of any other star. The mystery of these strange new objects was partially cleared up by Maarten Schmidt in 1963 when he showed that the spectral lines of a quasar have undergone an immense shift in wavelength.

Sandage continued to work on quasars and in 1965 introduced a method of identifying them by searching at an indicated radio position for objects emitting an excessive amount of ultraviolet or blue radiation. He found that many ultraviolet objects, which he named blue stellar objects or BSOs, were not radio emitters but could be still classed as quasars because they had the characteristic immense red shift first detected by Schmidt. He speculated that these might be older quasars that had passed beyond the radio phase of their life cycle. It is now known that the vast majority of quasars are not radio sources.