Sources told ESPN that personal terms were agreed between PSG and Hakimi more than a month ago and that the full-back pushed for the move to happen.
"I feel a great sense of pride today," Hakimi said. "After Spain, Germany and Italy, Paris Saint-Germain offers me the chance to discover a new championship with one of the most prestigious clubs in the world. I can't wait to meet my new teammates, the fans and experience the incredible colour and passion inside the Parc des Princes.
"I share the same big ambitions as the coaching staff and my teammates and will do everything I can to deliver what is expected of me."
PSG chairman and CEO Nasser Al-Khelaifi added: "This calibre of signing shows the level of our ambitions -- we continue to build something very special. Achraf may only be 22 years old and has already established himself as one of the most talented full-backs in world football -- these are the standards we set at the club. I know Achraf will have a fantastic career with us and the whole club wishes him every success in our colours."
Hakimi's departure will help Inter bring in needed money to help the club settle debts.
The defender played a key role in helping Inter claim their first league title in 11 years last season, contributing seven goals and 11 assists in Serie A.
The defender will become the latest new recruit at PSG after they signed Georginio Wijnaldum on a free transfer, and they are also set to complete the signing of Italy goalkeeper Gianluigi Donnarumma.