The Blues were hoping to complete the signing before deadline day, however they were given a deal sheet and completed it after the window closed at 11pm.
Drinkwater has joined for a fee of £35million – a club-record sale for the Foxes.
The deal surpasses the £32m Leicester received when N’Golo Kante joined the Blues last year.
Drinkwater has put pen to paper on a five-year deal and becomes the club’s sixth acquisition of the summer.
Speaking after his move, Drinkwater said: “I’m delighted to be a Chelsea player and can’t wait to get started.
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“It has been a long journey to get here but I am very happy and am looking forward to helping the club win more trophies.”
Blues technical director Michael Emenalo said: “Danny is not only a Premier League winner but also has Champions League experience which will be invaluable for us this season.
“He is a typically combative English midfielder with a cultured passing technique and his arrival significantly strengthens our midfield options.”
In a short statement posted on the club’s website, Leicester paid tribute to their former star.
It read: “Leicester City wishes to express its gratitude to Danny for his contribution to the team’s achievements over the past five years, as he leaves with the best wishes of everyone at the Football Club.”
Drinkwater, who was a product of the Manchester United academy, also had spells with Huddersfield, Cardiff, Watford and Barnsley before winding up at Leicester in 2012.
He went on to make 217 appearances for the Foxes and lifted the Premier League title in the 2015/16 season.
Despite getting a deal over the line in the early hours of this morning, Antonio Conte was left frustrated when a move for Ross Barkley fell through.
The Everton star underwent a medical, and while a £30m fee had been agreed with the Merseyside outfit, Barkley backed out at the last minute.