Sirigu, who spent last season on loan in Spain with Sevilla and Osasuna, moves on a free transfer after ending his PSG contract by mutual consent.
England international Joe Hart was Torino's first-choice keeper last season, but has returned to Manchester City after completing a loan spell.
"The club and the president made me feel important and I thank them for that," said Sirigu, 30.
Sirigu, capped 17 times by Italy, joined PSG from Palermo in 2011, but lost his place to Kevin Trapp at the start of the 2015-16 season.
Torino have signed Italy goalkeeper Salvatore Sirigu from Paris St-Germain.