"Angel Di Maria is a Juventus player," Juve said in a short statement on social media, before adding that he had "signed an employment contract until 30 June 2023".
The Argentina winger will earn a reported salary of seven million euros ($7.14 million) during his season in Turin.
The 34-year-old joins Juve ahead of the winter World Cup in Qatar into which his national team head as Copa America champions.
Di Maria left PSG after the French champions decided not to renew his contract last term, his position at the club downgraded by the arrival of Argentina teammate Lionel Messi last summer.
He played 295 times in all competitions for PSG, scoring 92 goals and racking up 112 assists in seven years in the French capital.
He won five league titles and five French Cups but missed out on the Champions League in 2020 when PSG were beaten in the final by Bayern Munich.
Juventus are also set for the return of France midfielder Paul Pogba as they try to bounce back from an underwhelming campaign in which they finished fourth, 16 points behind league winners AC Milan.
Pogba landed in Turin on Friday evening and is set to sign a four-year deal after being released by Manchester United.