The 20-year-old Italian scored just two goals last season after joining the Merseyside club in a £24.5million from Juventus last year.
Kean had also netted in two Carabao Cup ties, against Salford and Fleetwood, this term.
Kean said on psg.fr: “I am really proud and happy to become a Paris St Germain player. It is one of the best clubs in the world, as shown by their Champions League campaign last season where they reached the final.”
