The 20-year-old Kean has struggled for regular first-team opportunities under Everton manager Carlo Ancelotti.
The contracts of PSG strikers Edinson Cavani and Eric Maxim Choupo-Moting expired at the end of last season and Kean will bolster their attacking options which include Neymar, Kylian Mbappe and Mauro Icardi.
"I am really proud and happy to become a Paris Saint-German player," Kean told PSG's club website. "It is one of the best clubs in the world as shown by their Champions League campaign last season where they reached the final.
"I look forward to playing alongside some of the best players in the world."