Pietro was born in Brescia and was educated by local priest, including the Dominican friar Pavoni, and later at seminary, by the Theatine father Scarella, who had Jansenist leanings.

Thus in 1773, Tamburini moved to Rome and due to the help of Cardinal Mario Marefoschi, he obtained the post at the Collegio Irlandese, where the theologian Luigi Cuccagni also taught.

Tamburini was also appointed Prefect of Studies at the Austro-Hungarian College, today Collegio Cairoli, and published numerous texts, both of theology and defense of the liberal Habsburg rule in Lombardy.

With the death of Emperor Joseph II in 1790, the turbulence of the French Revolution, led the new reactionary Austrian government to expel Tamburini from the University of Pavia in 1794.

With the arrival of rule by Napoleon, he was rewarded "Knight of the Order of the Iron Crown", and in 1797 he was called there to teach a chair of moral philosophy and natural law.