Thomas Tuchel's side have paid £20m for Chukwuemeka's signature.
The18-year-old made 12 appearances in the Premier League last season for Steven Gerrard's side and is regarded as one of the hottest prospects in English football.
Chelsea announced Chukwuemeka's arrival on Thursday, having agreed a deal earlier in the week.
"It's been quite hectic but I couldn't get Chelsea out of my head the last few days so I'm just happy and relieved that it's all done," said Chukwuemeka.
"I'm so excited and just can't wait to get on the pitch, meet all the players and try to win games and trophies with Chelsea."
Chelsea chairman Todd Boehly added: "Carney is one of the most exciting young players in Europe so we are really looking forward to seeing him in action at Stamford Bridge. We are delighted to be able to bring him to Chelsea and add such a talented young individual to our squad for the new season and beyond."
Chukwuemeka is Chelsea fourth summer signing following the arrivals of Raheem Sterling, Kalidou Koulibaly and Chicago Fire goalkeeper Gabriel Slonina.
Chukwuemeka featured prominently as England u-19's won the European u-19 Championship this summer.