Morgan was educated at Amman Valley Grammar School, (now Ysgol Dyffryn Aman) Carmarthenshire, Wales before studying at the University College of North Wales, Bangor, for a Bachelor of Arts degree.
He obtained his doctorate with a thesis entitled A critical study of the works of Charles Edwards (1628-1691?)
He was a lecturer at the University College of Wales, Aberystwyth from 1969 before moving back to the Department of Welsh at Bangor in 1975, rising to become Reader (1983–1989).
As Vice-Chancellor, he was an ex officio Welsh Supernumerary Fellow of Jesus College, Oxford in 1997–1998 and 2003–2004.
[1] He is also a Founding Fellow of the Learned Society of Wales and is a Member of its inaugural Council.