Paredes has penned a two-year contract in the Italian capital with the option for a third.
The 29-year-old will be embarking on his second stint with Roma, having featured 54 times and scored four goals in his first spell at the Stadio Olympico between 2014 and 2017 before leaving for Zenit Saint Petersburg.
In four-and-a-half seasons at PSG, Paredes won the Ligue 1 title four times but fell out of favour and spent last season on loan at Juventus.
He played five times in Argentina's run to World Cup glory in Qatar.
"Coming back to Rome is always a special thing, but doing so now as a Roma player is even more special," the South American told the official Roma website.
"I'd like to thank the fans for welcoming me and Roma for bringing me back to the club where I launched my career in Europe. Last year was an incredibly happy one for me with the World Cup, so now I want to keep tasting success and I'm convinced I can do just that with this team."
Roma general manager Tiago Pinto added: "As soon as he heard that we were interested, Leandro made it clear that his target was to return to Roma.
"His strong willpower made us even more convinced that we should bring him back to the Giallorossi and we're delighted to see him back in Roma colours.
"Ever since his first stint here, he has matured and gained international experience, combined with his knowledge of Italian football and his technical attributes, we're sure this will all prove to be crucial and strengthen our squad."
