Born in Alba on 9 November 1925, Giovanni Coppa attended the seminary there before studying at the Catholic University of the Sacred Heart in Milan, where he obtained his doctorate in modern letters with a dissertation entitled: "The iconography of the Most Holy Trinity from the origins to the 14th century". He was ordained to the priesthood on 2 January 1949, and then served as a diocesan delegate for the aspirants of Catholic Action. In 1952, he entered the Roman Curia in the Apostolic Chancery. Coppa became the director of the Rome-based monthly retreats of the nuns of the Holy Family of Spoleto in 1954, and began working in the Vatican Secretariat of State in 1958.
During the Second Vatican Council (1962–1965), Coppa served as an expert for the Latin language. He was named an honorary canon of the chapter of St. Peter's Basilica in 1965, and assessor of the Secretariat of State on 19 November 1975. He was also Vice-Chaplain of the Palatine Guard of Honor and responsible of the Conference of Saint Vincent of Paul. When the Association of Saints Peter and Paul was instituted at the Holy See, the Secretariat of State named Coppa as its counselor. He wrote several works on Saint Ambrose, the Gospels, and the Fathers of the Church, and contributed to L'Osservatore Romano as well.
Coppa was named Apostolic Nuncio to Czechoslovakia on 30 June 1990, and then to both the Czech Republic and Slovakia on 1 January 1993. He retired from his post in Slovakia on 2 March 1994 and from the Czech Republic on 19 May 2001.