Nkunku had already agreed a pre-contract with the Premier League club in December and has now rubber-stamped his move to Stamford Bridge.
The 25-year-old has put pen to paper on a lucrative six-year contract with the Blues, who are embarking on a close-season overhaul as they look to bounce back from a dismal campaign.
"Chelsea is delighted to announce Christopher Nkunku will join the club from RB Leipzig ahead of the 2023/24 season," a statement on the Blues' website said.
Nkunku is one of the rising stars of European football and scored 23 goals in 36 games for Leipzig last season.
"I am incredibly happy to be joining Chelsea. A big effort was made to bring me to the club," Nkunku said.
"I am looking forward to meeting my new coach and team-mates and showing the Chelsea supporters what I can do on the pitch."
Nkunku, a graduate of the famed French national football academy at Clairefontaine, spent four years at Paris Saint-Germain before moving to Leipzig in 2019.
He made his name with the German club and was voted Bundesliga player of the season in 2021-22 after scoring 20 goals and providing 15 assists in the league.
The versatile forward bagged a further 23 goals this season to help Leipzig secure a third-place finish in the Bundesliga and scored in their German Cup final win against Eintracht Frankfurt.
'Creativity and versatility’
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."
Nkunku earned his France debut last year and has been capped 10 times.
He was ruled out of the 2022 World Cup in Qatar with a leg injury.
"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," Nkunku said.
"I am very excited for this challenge and will be proud to wear the Chelsea shirt."
Bidding farewell to Leipzig, Nkunku wrote a heartfelt message on the club's website:
"Now it's time for me to say 'Au Revoir' Leipzig. I am incredibly grateful to RB Leipzig and everyone at the club - my team, the coaching staff, the staff and most importantly the fans. I had four years in Leipzig which I will never forget," he said.
"I represented my country while at RB Leipzig, I have developed extremely well from a sporting and personal perspective and we have now been able to crown this time with two German cup wins.
"RB Leipzig will always have a permanent place in my heart. I hope there will be a chance in the future to come back to Leipzig as a guest and play in front of the great fans again."