Osheroff earned his Bachelor's degree in 1967 from Caltech, where he attended lectures by Richard Feynman and did undergraduate research for Gerry Neugebauer.

He married a biochemist, Phyllis Liu-Osheroff, in 1970.

Osheroff received a Ph.D. from Cornell University in 1973. He then worked at Bell Labs in Murray Hill, New Jersey for 15 years, continuing to research low-temperature phenomena in He. In 1987 he moved to the Departments of Physics and Applied Physics at Stanford University, where he also served as department chair from 1993-96. His research is focused on phenomena that occur at extremely low temperatures.

Osheroff joined the Laboratory of Atomic and Solid State Physics at Cornell University as a graduate student, doing research in low-temperature physics. Together with David Lee, the head of the laboratory, and Robert C. Richardson, Osheroff used a Pomeranchuk cell to investigate the behaviour of He at temperatures within a few thousandths of a degree of absolute zero. They discovered unexpected effects in their measurements, which they eventually explained as phase transitions to a superfluid phase of He. Lee, Richardson and Osheroff were jointly awarded the Nobel Prize in Physics in 1996 for this discovery.

Osheroff is left-handed, and he often blames his slight quirks and eccentricities on it. He is also an avid Photographer and introduces students at Stanford to medium-format film photography in a freshman seminar titled "Technical Aspects of Photography." In addition, he has taught the Stanford introductory physics course on electricity and magnetism on multiple occasions, most recently in Spring 2008, as well as undergraduate labs on low temperature physics.

Among his physics outreach activities, Osheroff participated in the science festivals for middle and high school students, is an official guest of honor at the International Young Physicists' Tournament 2013.