The Blues have captured the England full-back for £45 million on a five-year contract.
He becomes Chelsea's latest signing this summer following the acquisitions of winger Hakim Ziyech from Ajax and striker Timo Werner from RB Leipzig.
Chilwell is a product of Leicester's academy and made his debut at the Foxes in 2015, making a total of 123 appearances for the club and scoring four goals.
He told Chelsea's website: "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.
"He [Lampard] does play the younger players if they are good enough and just from speaking to him, I'm really excited to be here. I think the way the gaffer sets his teams up suits my game perfectly.
"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."
Chelsea director Marina Granovskaia added: "We are very pleased to have completed our third addition to our exciting squad for the coming season. Ben brings plenty of top-level experience playing in the Premier League, Champions League and at international level, despite his young age.
"We are confident Ben will adapt very quickly to being a Chelsea player and with the fixture programme for 2020-21 especially busy, he is a fantastic addition to the squad needed to challenge for honours."