Paul Cremona was born in Valletta on 25 January 1946 to Joseph and Josephine (née Cauchi). He has two siblings: an elder brother and a younger sister. Cremona was educated at the Montesseori School in Valletta and at the Lyceum in Ħamrun.
In September 1962 he joined the Dominican Order, and was professed on 29 September 1963. He studied philosophy and theology at the College of St Thomas Aquinas located at the Dominican priory at Rabat. Cremona was ordained as priest on March 22, 1969.
After his ordination, Cremona was sent to Rome for higher studies in Moral Theology. He is an alumnus of the Pontifical University of St. Thomas Aquinas Angelicum where in 1973 he obtained a doctorate in Sacred Theology (STD) with a thesis entitled The Concept of Peace in Pope John XXIII.
Cremona was elected Prior of Our Lady of the Grotto, Rabat in 1974, a position he held twice from: 1974-1980 and 1997-2003. He was Dominican Prior Provincial of Malta from 1981 to 1989.
In 1989 Cremona was appointed Parish Priest of Our Lady of Fatima Parish in Gwardamanġa, Pietà where he served until 1993; he then became responsible for the formation of Dominican novices and students at Rabat, an office he again held between 2004 and 2005. In 2005, Cremona become parish priest of Jesus of Nazareth in Sliema.
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). In 2007 as Archbishop, Cremona was appointed Grand Prior (for Malta) of the Equestrian Order of the Holy Sepulchre of Jerusalem with the rank of Knight Grand Officer.
As Archbishop of Malta, he is a popular preacher for Lenten sermons and is an author in theology and spirituality, including writings on the Creed and the Commandments. He also wrote some works with Patri George Frendo O.P., later Auxiliary Bishop of Tirana-Durrës, Albania.
Cremona was announced as the eleventh Archbishop of Malta on 2 December 2006. His consecration took place on 26 January at the Co-Cathedral of St. John the Baptist in Valletta. The Mass with the rites of consecration was led by the retiring Archbishop of Malta, Joseph Mercieca, who was the principal consecrator, assisted by the Apostolic Nuncio, Archbishop Felix del Blanco Prieto, and Bishop Patri George Frendo OP.
When the nomination of Cremona was made public on 2 December 2006, the Apostolic Nuncio Archbishop Felix del Blanco Priete announced to journalists and the Presbyterian council meeting at the Curia in Floriana: "Pope John Paul II was received in Malta with unforgettable enthusiasm as 'the second [Saint] Paul'. Today as per mandate of Pope Benedict XVI the diocese is being entrusted to another Paul."
The new Archbishop invoked Bishop Saint Augustine: "For you I am a Bishop but with you I am a Christian."
On 17 October 2014, the media revealed that Archbishop Cremona had submitted his resignation as Archbishop of Malta to the Vatican. His resignation was approved by the Holy See on the same day. His resignation came about after members of the episcopal curia said that the archdiocese lacked leadership. In August 2014, Archbishop Cremona was asked whether he would resign. He replied by saying, "I hold this position in obedience to the Pope's wishes and will only leave in obedience." On 18 October, Archbishop Cremona claimed that he started thinking of resigning two years prior, due to exhaustion. Archbishop Cremona was the first bishop of Malta to resign prior to the retirement age since the 19th century. Bishop Charles Scicluna was appointed apostolic administrator during the sede vacante; he was subsequently appointed the next Archbishop of Malta by Pope Francis on Friday, 27 February 2015. He was installed as Metropolitan Archbishop on 21 March 2015 in St Paul's Cathedral in Mdina.