Caprara was born at Bologna on 29 May 1733 to Count Francesco Raimondo Montecuccoli and Countess Maria Vittoria Caprara. He took his surname from the latter. He studied at the Collegio Nazareno in Rome and earned a doctorate in utroque iure at the Sapienza University of Rome on 23 September 1755.
Having entered the ecclesiastical state, he was appointed in 1755 referendary of the Tribunals of the Apostolic Signature and vice-legate of Ravenna from 1758 to 1761. Appointed titular archbishop of Iconio on 1 December 1766, he was consecrated bishop in the Quirinal Palace on 8 December 1766 by Pope Clement XIII.
Following his appointment as titular bishop, Caprara served as nuncio at Cologne from 1767 to 1775 where he dealt with the Febronian issue. In 1772 he visited Netherlands and United Kingdom.
Due to health problems, in 1775 Caprara was appointed nuncio at Lucerne, and in 1785 he was moved to Vienna, where he remained until 1793. The Vatican Secretary of State remained dissatisfied of his action in Vienna, where he for his pleaser and passive nature did not oppose the religious reforms undertook by Joseph II in order to make the Catholic Church in his empire the tool of the state, independent of the papacy.
In order to move him away from the nunciature in Vienna, on 18 June 1792 Caprara was promoted Cardinal Priest with the title of Sant'Onofrio. When Napoleon in 1796 conquered North Italy during the War of the First Coalition, Caprara, perhaps to protect his own estates in Bologna, took a stand in favor of the newly created Transpadane Republic even if such Napoleonic Republic had in agenda strong anticlerical measures. In this period he got the nickname of "Jacobin Cardinal". He supported the Treaty of Tolentino in 1997 which imposed terms of surrender on the Papal States.
Caprara participated to the Papal conclave in Venice and had good relations with Pope Pius VII with whom he traveled back to Rome. On 11 August 1800 he was appointed Bishop of Jesi in the Mark of Ancona.
When the Concordat of 1801 between Pope Pius VII and the French First Republic was concluded, Napoleon Bonaparte, then First Consul, asked for the appointment of a papal legate with residence in Paris. Napoleon's choice fell upon Cardinal Caprara; he may have expected in this way little or no opposition to his plans. Caprara was appointed legate a latere for France on 24 August 1801; he departed at once for his destination and arrived in Paris on 4 October.
During the negotiations which followed concerning the execution of the Concordat of 1801 he displayed a conciliatory spirit in dealing with the ten constitutional bishops who were to be appointed to as many of the newly established dioceses; in fact, he went contrary to specific instructions from Rome, under persistent pressure exerted by Napoleon Cardinal Caprara officiated at the Solemn restoration of public worship in the cathedral of Notre-Dame on Easter Day (18 April 1802), at which function the First Consul, the high officers of state, and the new ecclesiastical dignitaries assisted. In a letter written 18 August 1803, he protested against the Organic Articles added to the Concordat by the French Government.
In November 1801 the Archbishop of Milan Filippo Maria Visconti was invited by Tayllerand in Lyon to participate to the founding of the Napoleonic Italian Republic but on 30 December 1801 Visconti died there while sitting to a formal banquet. Napoleon arrived in Lyon on 11 January 1802 and designed Caprara as new Archbishop. Pope Pius VII concurred, so on 24 May 1802 Caprara was appointed Archbishop of Milan.
Caprara however retained his position as papal legate in France until his death and went on living in Paris. He visited Milan only from 2 April 1805 to 26 July 1805, to bless, on 26 May 1805, the Iron Crown which Napoleon placed on his own head in the Cathedral of Milan in his new dignity of King of Italy. During the absence of Caprara from Milan, the diocese was ruled by the Vicar general Carlo Bianchi who had to deal with the anticlerical commands of the Kingdom of Italy, such as the oath to the state Secretary of Cult by the teachers of the seminaries and the forced abolition of most confraternities.
Caprara lived in Paris until his death. The relations with Napoleon became more and more difficult, and his pleaser character bore to him dissatisfaction by the Pope. The situation degenerated in 1808 when the Napoleonic army entered in the Papal States. After that on 3 February 1808 General Miollis occupied Rome, Caprara resigned as legate, but contrarily to the papal order he did not left Paris. Still in 1809, when Pope Pius VII was already captive in Savona, Caprara pleaded the pope to support Napoleon. Declining health saved him from the embarrassment connected with the divorce and second marriage of Napoleon (April 1810).
Caprara died at Paris on 21 June 1810. In his last will his fortune was left to the hospital of Milan. Caprara had a solemn funeral for order of Napoleon, and his body was buried in the Panthéon of Paris (where remained until 1861) while his heart was buried in the Cathedral of Milan.Concordat et recueil des bulles et brefs de N. S. Pie VII. sur les affaires de l'Eglise de France (1802).