The 19-year-old was out of contract at the Parc des Princes at the end of the month but was expected to sign a new long-term deal with the Ligue 1 champions.
Simons's new contract in Paris would have seen him join PSV on loan for the 2022-23 season, but the Netherlands Under-19 international has instead left PSG on a permanent basis.
Simons has committed himself to a five-year contract at PSV until the summer of 2027, although PSG are reported to possess a €4m (£3.5m) buyback clause, which can be activated next year.
The teenager revealed to PSV's official website that Ruud van Nistelrooy and director John de Jong were key in his move to the club, saying: "They were very convincing and the feeling was right.
"PSV is a big club and I became more enthusiastic to make a move to Eindhoven after I had talks with the ambitious manager. He explained to me in detail the club's mission. I know what style of play he wants to introduce and what my role is.
"I need to get more games under my belt and I have a great opportunity to achieve my goal in this next stage of my career. I am ready and raring to go and prove myself at PSV. I am very happy with this move. I am fully convinced I have made the right decision."
Director of football De Jong added: "We saw him in action in all the games he played for Netherlands U19 and also watched him live at Youth League level in Leipzig, Paris, Brugge, Manchester and Sevilla.
"We are convinced of his potential. Xavi has got it all to develop into a key player for PSV and likes to share with us the path to fame and success."
Simons leave PSG having contributed just one assist in 11 senior appearances for Mauricio Pochettino's side since joining from Barcelona's academy in the summer of 2019.
The Dutchman collected a Ligue 1 and Coupe de France winners' medal during his time in the French capital, but he only featured six times in Ligue 1 last term - five of which came as a substitute.
Simons enjoyed a fruitful campaign at youth level, scoring four goals and setting up six more in seven UEFA Youth League appearances before missing the quarter-final defeat to Red Bull Salzburg through suspension.
The youngster has also earned six caps for the Netherlands' Under-19 side, contributing three goals and two assists and captaining the side on two occasions, and he follows Alphonse Areola, Marcin Bulka, Alexandre Letellier and Angel Di Maria out of the PSG exit door.
Simons may not be the only Dutch midfielder to leave PSG this summer, as the Ligue 1 champions are supposedly willing to offload Georginio Wijnaldum after his below-par first season.
Mutliple Premier League clubs are thought to be interested in signing Wijnaldum, but former teams Liverpool and Newcastle United are not expected to battle for his services.