"The club would like to thank 'Salva' for his steadfast professionalism and wish him all the best for the new challenges that await him in his homeland," a PSG statement read.
The 30-year-old had previously spoken of feeling forced out of PSG and he was delighted to complete his move to Torino.
"I am very happy to be part of this club," Sirigu told the PSG website. "I chose Torino because they wanted me strongly and for years have been pursuing a concrete project with exponential growth.
"The club and the president have made me feel important and I thank them for that. I am honoured to be part of a club that has a unique story."
PSG are among the European giants to have been linked with a move for AC Milan's 18-year-old goalkeeper Gianluigi Donnarumma, who has a year remaining on his San Siro contract.