The history of his education is unclear but he was called to Rome as a young man to assist Cardinal Giovanni Giacomo Panciroli.

[1] In 1665, at the age of 40, Baldeschi was elected Archbishop of Caesarea and only days later he was appointed Nuncio in Switzerland, a position he held until 1668.

[1] When Clement X died, Colonna participated in the conclave of 1676, which elected Pope Innocent XI.

It eventually elected Pope Innocent XII but without Colonna who was forced to leave because of illness.

Colonna never fully recovered and he died on 4 October 1691 and was buried at the church of the Propaganda Fide.