Donahue is from Pittsburgh, Pennsylvania. His father, Thomas Michael Donahue, was a prominent space scientist who taught at the University of Pittsburgh and later the University of Michigan.
Donahue attended Brown University, where he received a Bachelor of Arts degree in physics in 1985. At Brown, Donahue and his friends participated in environmental activism. Donahue attended the Massachusetts Institute of Technology for doctoral studies, graduating with a Ph.D. in meteorology in 1991.