The England international handed in a transfer request on Monday to try and force a move to Stamford Bridge, but the two clubs were still struggling to agree a fee heading into deadline day.
Chelsea’s first two offers worth £18million and £25m were rejected as Leicester looked to make in excess of £30m for the 27-year-old.
However, Chelsea’s third bid – understood to be worth £27m, plus add ons which would take it beyond £30m – was successful, with Antonio Conte landing an extra midfielder after selling Nemanja Matic to Manchester United for £40m.
Premier League Transfer Deadline Day: Latest deals
The deal sees Drinkwater reunited with N’Golo Kante, who he formed a title-winning midfield partnership with back in 2016.