Torricelli played for several Italian clubs throughout his career, but achieved prominence during his successful stint with Juventus, with whom he won several titles; he also had a spell in Spain with Espanyol.

At age 13, he was asked by Como to attend a youth regional championship (Allievi Regionali) with them but at the end of the loan he had to get back to his former amateur team US Folgore of Verano Brianza.

A player with a lot of heart and determination, despite his lack of skill, he was able to feature prominently in one of the best back-lines in Europe, and was capable of commanding all the roles in the Juventus defence, although his preferred position was at right-back.

Under manager Cesare Maldini, he was also a member of the Italian side at the 1998 World Cup, where Italy were eliminated on penalties by hosts and eventual Champions France in the quarter-finals, but he did not feature throughout the tournament.

Despite his lack of notable skills, class, or technical ability with his feet, he was a hard-working, tenacious, combative, reliable and determined team-player, who was both energetic and tactically intelligent; he also possessed significant physical strength, good elevation, and a strong mentality.

[3][9][10][11][12] In February 2009, Torricelli took his first managing role in football after being appointed as head coach of Tuscan Lega Pro Prima Divisione side Pistoiese.

On 23 June 2009, he was announced as the new head coach of Figline for the 2009–10 Lega Pro Prima Divisione campaign, the first in the Italian third tier for the small Tuscan club.