The France forward is new Chelsea manager Mauricio Pochettino's first summer signing.
Nkunku has signed a six-year contract at Stamford Bridge.
The 26-year-old scored 23 goals in 36 games for Leipzig last season as they finished third in the Bundesliga and won the DFB-Pokal for the second successive season.
Nkunku started his career at Paris Saint Germain, where he won three Ligue 1 titles before joining Leipzig in the summer of 2019.
He has won ten caps for the France national team but missed the Qatar 2022 World Cup through injury.
Nkunku, the Bundesliga’s joint top scorer this season with 16 goals, told Chelsea’s website: “I am incredibly happy to be joining Chelsea. 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."
Laurence Stewart and Paul Winstanley, Chelsea's co-sporting directors, said: "Christopher has proved himself one of the standout attacking players in European football over the past two seasons and will add quality, creativity and versatility to our squad.
"He has demonstrated his ability at the highest level with RB Leipzig and France and we look forward to him joining up with his new teammates ahead of the new season."
