The Portugal international leaves the Parc des Princes following an unsuccessful debut season under Christophe Galtier, who previously coached him during their time at Lille.
Sanches was a 2020-21 Ligue 1 title winner with Les Dogues, but his career has been blighted by injuries, and he scored two goals in 27 matches for PSG last term.
Sanches started a mere six games in the French top flight and just one in the Champions League, though, as he found himself below Marco Verratti, Vitinha and Fabian Ruiz in the midfield pecking order.
The former Benfica and Bayern Munich starlet is believed to have cost Roma €1m (£860,000) for his upcoming loan spell, and the €15m (£12.9m) purchase option will become mandatory if he plays in 60% of their games this term.
"I'm so happy to have joined this huge club. The Roma project really won me over and I feel that playing here is the right choice for me," Sanches told the official Roma website.
"It's so important for any player to feel the support of the fans. For me on my first day, the impact that I felt helped me understand how much these supporters love the team and that can only drive me forward to give my all to achieve success here."
Sanches was tipped to become one of the world's best midfielders after bursting onto the scene with Benfica and Portugal, winning the Euro 2016 crown with his nation as an 18-year-old.
The 25-year-old - who turns 26 on Friday - moved to Bayern that same summer, but he was unable to make his breakthrough at the Allianz Arena and also struggled to impress on loan with Swansea City during the 2017-18 season.
Sanches joins the Roma ranks only a few hours after his PSG teammate Leandro Paredes returned to Stadio Olimpico on a permanent deal, while Evan Ndicka, Houssem Aouar and Rasmus Kristensen have also signed for Jose Mourinho's side this summer.
"Renato Sanches is a player that we've been following for a long time," Roma's general manager Tiago Pinto added. "Despite that, he's still a young player and he's developed the habit of achieving success in every competition, both at club and international level.
"Renato has the technical and physical qualities that should see him slot seamlessly into our midfield, making it even more competitive."
Sanches could make his first appearance for Roma when the Giallorossi open their 2023-24 Serie A campaign at home to Salernitana on Sunday evening.