Born at Ystradgynlais, Brecknockshire, Wales, Daniel was educated at Pontardawe Grammar School, Amman Valley County School and University of Wales, Aberystwyth, where he gained a first-class degree. He obtained a D.Phil. from Jesus College, Oxford. In 1940 he married Valerie, daughter of Richard Lloyd George. They had one son and two daughters.
In 1969 he returned to Aberystwyth to become Principal of the University College of Wales, and was knighted the same year. He held the post for ten years. In 1977 he was appointed a Lieutenant of Dyfed. In 1982 he was appointed Chairman of the Welsh Fourth Channel Authority, having been one of the prime movers in its creation.
- Meic Stephens (20 January 2003). "Sir Goronwy Daniel". The Independent. Retrieved 13 June 2019.
- National Library of Wales (1977). Annual Report - National Library of Wales. p. 25.
- Gwynfor Evans (1996). For the Sake of Wales: The Memoirs of Gwynfor Evans. Welsh Academic Press. p. 229. ISBN 978-1-86057-006-3.
- The Rt Hon Lord Morris of Aberavon (1 September 2011). Fifty Years in Politics and the Law. University of Wales Press. p. 193. ISBN 978-0-7083-2636-7.