Albani was born in Rome into a noble family that produced a number of clergy. His great-uncle was Pope Clement XI and three other relatives were prominent cardinals: two nephews of Pope Clement, Annibale Albani and Alessandro Albani, and Alessandro's nephew Gianfrancesco Albani, who was Giuseppe's uncle. He studied for the priesthood in Siena, but in his early twenties he returned to Rome to be a domestic prelate for Pope Clement XIV. He gained experience in the practice of canon law. He held major offices in the Roman Curia from a relatively early age. During the French occupation of Rome at the end of the 18th century, he took refuge in Vienna, where he became allied with the Habsburg monarchy. The Habsburgs claimed the right to exercise over papal election, the jus exclusivae, and he served as their intermediary in subsequent papal conclaves when they chose to exercise that right. The French invaders had removed many works of art from the Villa Albani, which had been built for Alessandro Albani, who filled it with his collection of antiquities and ancient Roman sculpture. In 1815 Giuseppe Albani reclaimed them but sold them rather than pay the costs of transporting them to Rome. Some remained in Paris and several entered the collection of Ludwig I of Bavaria. On 20 May 1817 he was appointed Prefect of the Congregation for Bishops and Pius VII made him a cardinal in 1818, assigned the titular church of San Cesareo in Palatio. In the conclave of 1823, he presented the veto against the election of CardinalAntonio Gabriele Severoli on behalf of Emperor Francis I of Austria. In the 1829 conclave, though Albani was absent from the early ballots, his support for Pius VIII proved significant. In the conclave of 1830, Albani played a significant role but did not see his candidate Bartolomeo Pacca succeed. As Cardinal Protodeacon he announced the elections of Pope Pius VIII in 1829 and Pope Gregory XVI in 1830 and crowned both with the triple tiara. Albani's other appointments included Secretary of Secret Domestic Briefs on 30 January 1824, as Legate in Bologna on 10 December 1824, Secretary of State to Pius VIII from 31 March 1829 until 30 November 1830, and as Secretary of Apostolic Briefs from 15 April 1829 until his death. He was also Librarian of Holy Roman Church beginning on 23 April 1830. In 1831 he was also appointed Legate in Urbino and Pesaro, and was the commissary extraordinary charged with reestablishing order in the Legations. He died in Pesaro on 3 December 1834. He was buried in the family chapel in the cloisters of the Church of San Pietro in Urbino.
