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".

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.

When the Association of Saints Peter and Paul was instituted at the Holy See, the Secretariat of State named Coppa as its counselor.

On 1 December 1979, Coppa was appointed delegate for the Secretariat of State's pontifical representations and titular archbishop of Serta.

He received his episcopal consecration in Saint Peter's Basilica on 6 January 1980 from Pope John Paul II with Archbishop Eduardo Martínez Somalo and Bishop Ferdinando Maggioni serving as co-consecrators.