Born at Clifden on 4 January 1944 to Cecil Canny and Helen Joyce, he was educated at Kilfenora national school, St. Flannan's College, Ennis, and University College Galway (now NUI Galway) from where he graduated with a BA in 1964, and an M.A. in 1967.
Since the mid-1970s, Canny has been the leading authority on early modern Irish history.