According to media reports, the deal is worth around 70 million euros (£60 million) and includes the return of 26-year-old international midfielder Renato Sanches to Benfica on loan.
"I'm very proud to be joining Paris Saint-Germain, a very ambitious club," said Neves in a statement released by PSG, which described him as a "hard worker, a complete and versatile player".
Neves, who has nine caps and played two group matches for Portugal at Euro 2024, is expected to add creativity to the PSG midfield, alongside Vitinha, Fabian Ruiz and Warren Zaire-Emery.
"Joao is one of the most talented players in Portugal and in the world," said PSG's Qatari president Nasser Al-Khelaifi.
Neves is the Paris club's second summer recruit after Russian goalkeeper Matvey Safonov.
