Giuseppe Paupini was born in Mondavio, Italy. He was educated at the local seminary of the diocese of Fano and later at the Pontifical Regional Seminary "Pio XI" and at the Pontifical Lateran University where he earned a doctorate in canon law. He was ordained on 19 March 1930 in Fano. He worked in the diocese of Fano and as a faculty member of its seminary from 1932 until 1939. He entered the diplomatic service of the Holy See in 1939 as attaché of the nunciature to France and later as secretary of the nunciature to Italy. He was chargé d'affaires of the nunciatures in Honduras, Nicaragua and Cuba between 1947 and 1951. He was promoted to counselor of nunciature in 1951. Between 1952 and 1956 he fulfilled pastoral assignments in the Diocese of Rome.

He was appointed Titular Archbishop by Pope Pius XII and appointed internuncio to Iran and at the same time Apostolic administrator of Ispahan of the Latins. He was consecrated on 26 February 1956 by Cardinal Valerio Valeri.

He was transferred as Nuncio to Guatemala and El Salvador on 25 February 1957.^[1] In 1959 he was appointed Nuncio to Colombia. He attended the Second Vatican Council in the 1960s.

He was made Cardinal-Deacon of Ognissanti in Via Appia Nuova by Pope Paul VI on 28 April 1969. He was appointed Major Penitentiary of the Apostolic Penitentiary on 21 March 1973. He took part in the conclaves that elected Pope John Paul I and Pope John Paul II in August and October. He opted for the order of Cardinal-Priests on 30 June 1979. He resigned the post of Major Penitentiary on 8 April 1984 at the age of 77. He was Camerlengo of the College of Cardinals from 22 June 1987 until 2 May 1988. He died on 18 July 1992.