De Giorgi was born 6 September 1930 in Vernole, in Apulia (Southern Italy). He was ordained as a priest in 1953 and was secretary to Bishop Francesco Minerva of Lecce. He also served as diocesan chaplain for the Teachers' Movement of Catholic Action. 1958 when he became parish priest of Our Lady of Grace in Santa Rosa. In 1973, he was made Titular Bishop of Tulana and an auxiliary bishop of Oria. He became Bishop of that see on 17 March 1978. His pastoral ministry was characterized by the accentuation of the spiritual, commitment to the formation of the clergy, the promotion of the laity. Attentive to ecumenical and interreligious dialogue, he was also particularly sensitive to social problems, especially those concerning the family, youth and the protection of life, and has directed special attention to the situation of the marginalized.
In 1981, he was made archbishop of Foggia. From 1987 to 1990, he served as archbishop of Taranto. In 1990, he was appointed General Chaplain of Italian Catholic Action, a position which he held until becoming archbishop of Palermo in 1996. At the same time, he was also elected President of the Sicilian Episcopal Conference. He was often outspoken in his condemnation of organized crime and the mafia. He has visited emigrants from Palermo in the Italian communities in Melbourne, Australia, Chicago and Milwaukee in the United States of America, in Toronto, Canada and London in England.
De Giorgi was named a Cardinal-Priest of Santa Maria in Aracoeli in 1998. He was one of the cardinal electors who participated in the 2005 papal conclave that selected Pope Benedict XVI.
He retired as Archbishop of Palermo on 19 December 2006 and was succeeded by Archbishop Paolo Romeo, who had been apostolic nuncio to Italy and San Marino.
Cardinal De Giorgi is noted as a writer and journalist. He has authored several religious publications, including Un servizio di amore per una Chiesa di frontiera.
In the Roman Curia, he serves in the Congregation for the Clergy, the Council for the Laity, and the Council for the Family.
Pope Benedict XVI appointed him to a commission to investigate leaks of reserved and confidential documents on television, in newspapers, and in other communications media. It first met on 24 April 2012.
In May 2013 Pope Francis designated De Giorgi, as Archbishop Emeritus of Palermo, his representative to officiate at the beatification of Father Pino Puglisi, killed by the mafia in 1993. As generally the Pope chooses either the Prefect of the Congregation for the Causes of Saints or the Cardinal Secretary of State, this was seen as both unprecedented.
On 19 September 2015, Pope Francis named De Giorgi as his Special Envoy to the concluding celebration of the fifth centenary of the creation of the Diocese of Lanciano, Italy, which is now the Archdiocese of Lanciano-Ortona, held on 22 November 2015.