He studied philosophy and theology at the College of St Thomas Aquinas located at the Dominican priory at Rabat.

After his ordination, he studied at the Pontifical University of St. Thomas Aquinas Angelicum and earned his doctorate in sacred theology (STD) in 1973 with a thesis entitled The Concept of Peace in Pope John XXIII.

Cremona held other offices in the Archdiocese of Malta, including Archbishop's Delegate for Consecrated Life, assistant spiritual director at the Seminary at Tal-Virtù, Rabat, member of the Presbyterial Council, and president of the Council of Maltese Religious Major Superiors (KSMR).

He received his episcopal consecration on 26 January 2007 at the Co-Cathedral of St. John the Baptist in Valletta from the retiring Archbishop of Malta, Joseph Mercieca, assisted by the Apostolic Nuncio, Archbishop Félix del Blanco Prieto, and Bishop George Frendo, Cremona's former schoolmate.

"[2][3] On 17 October 2014, Cremona submitted his resignation as Archbishop of Malta and Pope Francis approved it the same day.

Charles Scicluna was appointed Apostolic Administrator and later Archbishop of Malta by Pope Francis on 27 February 2015.