[6] Murphy earned his undergraduate degree in medicine at University College Cork (UCC), graduating in 1973.

He undertook further studies at the Royal Postgraduate Medical School in London, England.

[7] From 1984 to 1992, Murphy taught medicine and pharmacology at the University of Chicago in the United States.

[7] In 1992, he returned to Ireland and UCC, where he had been appointed Professor of Clinical Pharmacology and Therapeutics.

[9] He stepped down as president in 2017, after ten years leading UCC, and was succeeded by Patrick O'Shea.