Barrasso was born in Reading, Pennsylvania, in 1952, the son of Louise M. (née DeCisco) and John Anthony Barrasso, Jr. He is of Italian descent. He is a 1970 graduate of the former Central Catholic High School, which in 2011 merged with Holy Name High School to form Berks Catholic High School. Barrasso attended Rensselaer Polytechnic Institute (where he became a member of Phi Kappa Tau fraternity) for two years before transferring to Georgetown University in Washington, D.C., graduating Phi Beta Kappa in 1974 with a Bachelor of Science degree in biology. He received his M.D. degree from Georgetown University School of Medicine in 1978. He conducted his residency at Yale Medical School in New Haven, Connecticut.