The Blues have landed the 2015/16 Premier League champion in a fee believed to be in excess of £30million.
Drinkwater, 27, joined the Foxes from Manchester United in 2012 and has since enjoyed a stunning rise with the club, which peaked when they won the title under Claudio Ranieri.
He will now link up with former team-mate N’Golo Kante in the heart of the Chelsea midfield.Drinkwater said: ‘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.
Chelsea’s technical director Michael Emenalo added: ‘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.’The Blues also landed Davide Zappacosta from Torino in what was a dramatic deadline day at Stamford Bridge.