The left-back has signed a five-year contract with Frank Lampard's team after they reached an agreement with the Foxes this week.
"I am delighted to be joining Chelsea at this very exciting time for the club," Chilwell told the club's website.
"I’m looking forward to being a part of this young, dynamic squad led by Frank Lampard as we challenge for honours next season. 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 came through Leicester's youth academy to become a key player for the senior team, making 123 appearances and helping them to win the Premier League title in 2016.
"We are very pleased to have completed our third addition to our exciting squad for the coming season," director Marina Granovskaia said.
"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."
Further additions are expected as the Stamford Bridge outfit made progress in their pursuit of Bayer Leverkusen playmaker Kai Havertz this week, having agreed to match the Bundesliga team's £90m ($118m) asking price.
They are also set to announce the signing of 21-year-old defender Malang Sarr for free after his contract with Nice expired at the end of the 2019-20 campaign.
The French centre-back, who was wanted by Arsenal, Schalke and Leverkusen among others, has agreed a five-year contract with the London club but will likely be sent out on loan for next season.
Chelsea are expected to strengthen even further at the back this week, as 35-year-old Thiago Silva is close to joining following his departure from Paris Saint-Germain as his contract expired after their Champions League final defeat to Bayern Munich.
They have already waved goodbye to Pedro and Willian after their contracts expired. The Spain international completed a switch to Roma this week, while Willian joined Arsenal on a three-year deal earlier this month.