Joseph Soueif was born in the Lebanese town of Chekka, a coastal village in northern Lebanon, in Batroun District. He completed his secondary studies at the patriarchal seminary of St. Maron in Ghasim in 1982, and later studied theology at Holy Spirit University of Kaslik, graduating in 1987. He was ordained to the priesthood at the age of twenty-five on 3 September 1987 by the Maronite Archbishop of Tripoli Antoine Joubeir. In 1992 Soueif received his doctorate at the Pontifical Oriental Institute in Rome.
His appointment as Archbishop of Archeparchy of Cyprus was on 29 October 2008. The solemn consecration took place on 6 December 2008 being his principal consecrator His Beatitude Maronite Patriarch of Antioch, Nasrallah Boutros Sfeir and the Archbishops Boutros Gemayel of Cyprus and Georges Bou-Jaoudé of Tripoli acted as co-consecrators bishops.