Farrell was born in Manchester in 1929. He was educated in Ireland at University College Dublin and Harvard University. In 1955 he joined the administrative staff of University College Dublin. In 1966, he began lecturing in the department of ethics and politics there. He went on to become senior lecturer in politics and in 1985 he became Associate Professor of Politics. He retired from academia in the mid 1990s.
Farrell has also enjoyed a successful career as a media commentator. He has written articles for the Irish Press and the Irish Independent. During the 1950s he worked with Radio Éireann and in 1962 he joined the newly established Telifís Éireann. Since then he has presented RTÉ's main programmes of comment and analysis - Broadsheet, Newsbeat, Seven Days, Today Tonight and Prime Time. Farrell has also covered major events at home and abroad, and has presented the results programmes for ten Irish general elections.
Farrell has also written a number of books on Irish political history, including Chairman or Chief?, The Founding of Dáil Éireann and a biography of Sean Lemass.