After Blairs, he completed his ecclesiastical studies at the Royal Scots College (el Real Colegio de los Escoceses), Valladolid.
He was ordained to the Priesthood for the Archdiocese of St Andrews & Edinburgh in the college chapel on 17 March 1956 by Bishop Joseph McGee.
In 1999, Monsignor Ian Murray was nominated ninth Bishop of Argyll & the Isles by Pope John Paul II.
He was consecrated by Archbishop Keith Michael Patrick O'Brien on 7 December that year, the feast of St Ambrose, a patron of the Royal Scots College.
On 15 December 2008, reaching 75 years of age, in accordance with Canon Law, Bishop Murray submitted his resignation to Pope Benedict XVI, who appointed the Very Reverend Monsignor Joseph Anthony Toal, the Rector of the Royal Scots College, to succeed him as tenth Bishop of Argyll & the Isles.