"I am incredibly happy to be joining Chelsea," Nkunku told the club's website. "A big effort was made to bring me to the club and I am looking forward to meeting my new coach and teammates and showing the Chelsea supporters what I can do on the pitch.
"Having played in Ligue 1 and the Bundesliga, I now want to play in the Premier League, one of the strongest leagues in the world. I am very excited for this challenge and will be proud to wear the Chelsea shirt."
Nkunku, 25, has been one of the standout performers in Germany for a number of years and was named Bundesliga Player of the Season and German PFA Player of the Season in the 2022-23 campaign.
He also helped Leipzig win back-to-back German Cups and contributed 23 goals in all competitions last season.