Brans was born in Dallas, Texas, and graduated in 1957 from Loyola University, Louisiana. Having obtained his PhD from Princeton in 1961, he returned to Loyola in 1960 and in 1970 was appointed professor of physics.

Brans has worked mainly in the field of general relativity. He is best known for his production with Robert Dicke in 1961 of a variant of Einstein's theory in which the gravitational constant varies with time. A number of very accurate measurements made in the late 1970s has failed to detect this and some of the other predictions made by the Brans–Dicke theory.