Richardson was educated at Virginia State University and at Duke University, North Carolina, where he obtained his PhD in 1966. He moved immediately to Cornell and was appointed professor of physics in 1975.

In the early 1970s work with Douglas Osheroff and David Lee revealed that, contrary to expectations, helium-3 became a superfluid at a temperature of 0.0027 degrees above absolute zero. Richardson shared the 1996 Nobel Prize for physics with Osheroff and Lee for his work in this field.