Sources told ESPN on Friday that the deal was close to being done after Leicester dropped their £80 million valuation, and the two clubs eventually agreed a deal for £50m.
"'I am delighted to be joining Chelsea at this very exciting time for the club," Chilwell said. "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.
The move is a blow to the Midlands club who were hoping to hold onto the England international.
The high valuation came from Chilwell's contract with the club which was to last until 2024 and Brendan Rodger's eagerness to keep him.
However, the full-back's desire to move and the financial pressures of the coronavirus pandemic eventually led Leicester to the negotiating table.
Frank Lampard's side may not be able to use him right away as an heel injury could prevent him from participating in the start of the season.