He was the son of Prospero Costaguti (Marquis of Sipicciano and of Rocca Elvezia) and his first wife Paola Costa.
Thereafter he was appointed Commissary General of Umbria and Marca before obtaining a doctorate utroque iure in 1638 which qualified him to be appointed referendary of the Tribunals of the Apostolic Signatura of Justice and of Grace.
At only 31, Costaguti was elevated to Cardinal in 1643 and was installed as Cardinal-Deacon at the Church of Santa Maria in Portico Octaviae.
[2] He was regularly in the company of Pope Innocent and contemporary, John Bargrave, suggested he was also popular among the College of Cardinals and the people of Rome because of his good humour and generosity.
[3] Pope Innocent made him Legate in Urbino from 1648 to 1651 after which he opted for the title of Cardinal-Deacon of Sant'Angelo in Pescheria in 1652.