The great-great-grand-nephew of Pope Pius V, he received his doctorate in law from the University of Perugia and was appointed private chamberlain to Pope Urban VIII. His career in the Roman Curia resulted in appointments as governor of several cities of the Papal States including Rome, then as vice-camerlengo from 15 April 1655 until 18 October 1656, when he was appointed to the titular position of Latin Archbishop of Corinth. Fortified by the title, he was sent as nuncio extraordinary to Philip IV of Spain to establish peace among the Christian princes, 27 October 1656. With the Treaty of the Pyrenees signed in 1659, he remained in Madrid as ordinary nuncio until 1664. When he was recalled to Rome and made cardinal in the consistory of 14 January 1664, with the titulus of S. Anastasia, he brought with him the auditor of the papal legation at the court of Madrid, the antiquarian Raffaello Fabretti, who took advantage of Bonelli's leisurely return through the south of France to extend his knowledge of Roman antiquities.
- Title of S. Anastasia
- Harry B. Evans, Aqueduct Hunting in the Seventeenth Century: Raffaele Fabretti's De Aquis Et Aquaeductibus Veteris Romae 2002, Introduction.
- As, e.g. the "clumsy and disjointed effects" noted by Robert Enggass, "New Attributions in St. Peter's: The Spandrel Figures in the Nave" The Art Bulletin 60.1 (March 1978:96-108); "At other times Rainaldi seems to have been unable to provide the direction and designs such sculptors needed. The tomb of Cardinal Carlo Bonelli in S.M. sopra Minerva, executed in the early 1670's, documents his helplessness on one such occasion." (Howard Hibbard, "Palazzo Borghese Studies - II: The Galleria" The Burlington Magazine 104 No. 706 [January 1962:9-20] p. 16).
- Cardinals of the Holy Roman Church: Carlo Bonelli