Bishop Moore was born on 12 January 1942 in the parish of Harold's Cross, Dublin, in the Archdiocese of Dublin, the second son of John and Mary Moore (née Broughal). He was educated at the Christian Brothers Secondary School, Synge Street,[1] Dublin from 1955 to 1959.[2] In 1960 he became a member of the SMA. From 1960 to 1966 he studied Philosophy and Theology at the SMA Major seminary at Dromantine House, Newry, Co Down. Right Reverend Eugene Doherty, Bishop of Dromore, ordained him to the priesthood on 20 December 1965 in St Colman's Cathedral, Newry.