The France Under-21 international has signed a five-year contract with the Bundesliga outfit after failing to nail down a regular starting place in Paris.
It is believed Leipzig have paid an up-front fee of €13m, with a further €2m potentially due in bonuses.
Nkunku, a midfielder developed at PSG, made 22 Ligue 1 appearances under Thomas Tuchel last term, starting 13 times.
In arriving at Leipzig, he becomes the third new addition to Julian Nagelsmann's squad, after Hannes Wolf and Luan Candido.
"I have heard a lot about the club and am convinced that the way football is played here suits me very well," Nkunku said.
"I already know some of my new team-mates: I've played with Jean-Kevin Augustin in Paris, and with Dayot Upamecano and Nordi Mukiele for France.
"I'm optimistic that I can come here and settle quickly."
Nkunku is not the only young player on the way out of PSG.
The French champions have allowed teenage attacker Virgiliu Postolachi to leave for Ligue 1 rivals Lille, where he has agreed a four-year contract.