The Premier League champions who chased the midfielder for most of the summer, finally had a third bid accepted on Thursday evening.
Leicester had previously rejected a £23m bid from Antonio Conte’s side, but the Blues managed to get the deal over the line at the last minute.
Drinkwater has said he is relishing the chance at Stamford Bridge after passing a medical.
“I’m delighted to be a Chelsea player and can’t wait to get started. 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,” Drinkwater said after the move was made official.
The 27-year-old is Chelsea’s sixth signing of the summer.