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.

South Yorkshire Police officers were called to High Melton College at about 14:45 GMT on Tuesday where workmen had found what appeared to be a body.
Dark and cold conditions prevented officers from accessing the body so the scene was guarded overnight.
Detectives are working with Yorkshire Water, underwater search teams and crime scene officers to determine the circumstances surrounding the incident.
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High Melton is a campus of Doncaster College.

Alan Mason, 45, of Endmoor, Kendal, knew he had the virus for five years when he started a sexual relationship with the woman, from Barrow.
Carlisle Crown Court heard he only told her when she began to feel unwell after contracting the disease herself.
He was jailed for two years and eight months after admitting causing the woman, 39, grievous bodily harm.
After the hearing, Det Con Damian West, of Cumbria Police, said: "This is a unique case for Cumbria and the sentencing imposed highlights the disregard Mason had for his actions.
"Even though the victim has to live with this virus, modern medication means there should be no impact on life expectancy.
"However, the virus has a significant day to day impact on those who have to live with it."
Torino have signed Italy goalkeeper Salvatore Sirigu from Paris St-Germain.
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A body has been found in a sewage tank at a Doncaster college.
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A Cumbrian man who is HIV positive has been jailed for infecting his former partner with the virus.