Incrocci was born in Brescia, into a family including several actors, such as his sister Zoe, and spent his youth moving with them to numerous places of Italy.
His first work in the cinema world was a dubber for Mario Monicelli's first movie, I ragazzi della Via Paal (1935).
He spent the first four years of World War II in France, as a prisoner of the French Army first and, later, of the Wehrmacht.
These include some of the most famous of all, such as Sergio Leone's The Good, the Bad and the Ugly, Mario Monicelli's I soliti ignoti and many Totò movies.
As an actor, he took part to La terrazza by Ettore Scola (screenplay by Age & Scarpelli, of course) and Ecce Bombo by Nanni Moretti.