Bertello was ordained a priest on 29 June 1966 by Bishop Albino Mensa. He earned a licence in pastoral theology and a doctorate in canon law. He went on to attend the Pontifical Ecclesiastical Academy where he studied diplomacy.
He entered the diplomatic service of the Holy See in 1971, and worked until 1973 in the nunciature to the Sudan, which was also the apostolic delegation for the Red Sea region. From 1973 to 1976, he was secretary at the nunciature to Turkey, becoming a Chaplain of His Holiness on 9 February 1976. He was secretary in the nunciature to Venezuela from 1976 to 1981, and served with the rank of auditor in the Office of the Organization of the United Nations in Geneva from 1981 to 1987. In 1987, he headed the delegation of observers of the Holy See to the Conference of Foreign Ministers of the Movement of Non-Aligned Countries in Pyongyang, North Korea where he was the first Catholic priest to be able to visit the small Catholic community of that country, isolated since the Korean War.
On 17 October 1987, Pope John Paul II named him Titular Archbishop of Urbs Salvia and appointed him Apostolic Nuncio to Ghana, Togo and Benin. He was consecrated on 28 November by Cardinal Secretary of State Agostino Casaroli, with Bishops Albino Mensa and Luigi Bettazzi as the principal co-consecrators. On 12 January 1991, he was transferred to Rwanda, where he witnessed the buildup to the Tutsi Genocide in 1994. He was the first diplomatic figure to withdraw when the genocide erupted following the assassination of President Habyarimana on the 6th April.
In March 1995, John Paul II appointed him to the post of Permanent Observer of the Holy See to the United Nations in Geneva from 1997, with the same role at the World Trade Organization. Upon his appointment Bertello negotiated the ingress of the Holy See as permanent observer, in the World Trade Organization, becoming its first representative.
On 27 December 2000, the Pope entrusted him with another task, that of Apostolic Nuncio to Mexico. On 30 July 2002, he received the Pope arriving on an apostolic visit in the country for the canonisation of Juan Diego Cuauhtlatoatzin. In 2007, Bertello was appointed to the prestigious post of apostolic nuncio to Italy and the Republic of San Marino by Pope Benedict XVI.
In 2007 he was awarded with the Grand Cross of the Mexican Order of the Aztec Eagle and in 2008 Archbishop Bertello was awarded the Knight Grand Cross of the Order of Merit of the Italian Republic.
On 3 September 2011, Pope Benedict XVI appointed Archbishop Bertello President of the Pontifical Commission for Vatican City State and President of the Governorate of Vatican City State, offices assumed on 1 October 2011, his 69th birthday. On 6 January 2012, Pope Benedict announced that Archbishop Bertello would be created cardinals. He was created Cardinal-Deacon of Santi Vito, Modesto e Crescenzia on 18 February. On 21 April Cardinal Bertello was appointed, for the usual five-year period, a member of the Congregation for the Evangelization of Peoples, the Congregation for Bishops and the Pontifical Council for Justice and Peace.
He was one of the cardinal electors who participated in the 2013 papal conclave that elected Pope Francis.
On 13 April 2013 he was appointed to a group cardinals established by Pope Francis to advise him and to study a plan for restructuring the Roman Curia.