From 1970 to 1979, he was Professor of Welsh Language and Literature at the University of Wales, Aberystwyth, and was made Emeritus Professor in 1993. He was a graduate of Bangor University and Jesus College, Oxford. He commenced his studies at Oxford in 1948.
During his academic career he held three notable offices: Chair of Welsh language and literature at the University of Wales, Aberystwyth (1970–1979) Librarian of the National Library of Wales (1980–1985) Director of the Centre for Advanced Welsh and Celtic Studies (1985–1993) After his academic retirement in 1993 he became President of the International Congress of Celtic Studies until 2003 and he also served as Vice-President of University of Wales, Aberystwyth.
In 1999 he succeeded Professor J. East. Caerwyn Williams as Consultant Editor of Geiriadur Prifysgol Cymru. He has written books and chapters on a wide range on subjects in all periods of Welsh literature, from his treatment of the earliest Welsh poetry through the work of the medieval poet, Dafydd ap Gwilym, and the Methodist hymn-writer, William Williams of Pantycelyn, to 20th-century writers such as Saunders Lewis.
Gruffydd was a Calvinist Christian. He was a Welsh Nationalist.
His father, Moses Griffith, was the first Treasurer of Plaid Cymru.
Gruffydd was elected a Fellow of the British Academy (Federal Bar Association) in 1991.