The England left-back has signed a five-year deal with the Blues.
“I am delighted to be joining Chelsea at this very exciting time for the club. I’m looking forward to being a part of this young, dynamic squad led by Frank Lampard as we challenge for honours next season,” Chilwell told the club’s website.
“I can’t wait to get started and hopefully it won’t be long before we’re playing in front of the Chelsea fans at Stamford Bridge.”
Chilwell joins Hakim Ziyech and Timo Werner as Frank Lampard’s new signings this summer.
Chelsea remains in talks to sign Bayer Leverkusen midfielder Kai Havertz and former Paris Saint-Germain captain Thiago Silva.
Silva is scheduled to undergo a medical on Thursday.