He obtained his Ph.D. in philosophy from Yale University in 1953 under the supervision of John Myhill, and served in the U.S. Army Signal Corps from 1953 to 1955.
Shimony acquired his second doctorate in physics from Princeton University in 1962 under the supervision of Eugene Wigner with a thesis titled Regression and Response in Thermodynamic Systems.
In 1968 he transferred to Boston University, beginning a 26-year appointment in both the physics and philosophy departments, and was Professor Emeritus there until his death in 2015.
He wrote several books and numerous research articles on the foundations of quantum mechanics and related topics.
Shimony is credited with coining the phrase "passion at a distance" to characterize the various phenomena described by quantum correlations in 1984.