Born in Shanghai where his father, a Dundalk man, captained a ship on the Yellow River, Byrne was evacuated with his mother to Australia on the outbreak of World War II.
He studied Early Irish History at University College Dublin where he excelled, graduating with first class honours.
He studied Paleography and Medieval Latin in Germany, and then lectured on Celtic languages in Sweden, before returning to University College in 1964 to take up a professorship.
He was joint editor of the Royal Irish Academy's New History of Ireland (9 volumes).
A festschrift in his honour, Seanchas (1999), was published under the editorship of his former student Alfred P. Smyth.