The England international finally became a Chelsea player in the early hours of Friday morning after the defending champions agreed a fee with Leicester City.
Drinkwater has signed a long-term deal with the west London side and has become the sixth summer signing at Stamford Bridge.
The 27-year-old was part of the famous Leicester team that won the Premier League title under Claudio Ranieri in the 2015-16 season.
The former Manchester United midfielder will be tasked with helping to reinforce Antonio Conte’s midfield following Nemanja Matic’s move to Manchester United last month.
And Drinkwater admitted that he is grateful that his summer transfer went through after a dramatic deadline day for the England star.
“My emotions have been all over the place,” Drinkwater told Chelsea’s website.
“There has been frustration, excitement, I have been nervous and I am just grateful the transfer is done.
“Leicester has been great for me but I am looking to carry on from the season before last when we won the Premier League there and I want to win more trophies, which Leicester have understood and where better to do it than Chelsea.
“I am at a good age now to kick on. I have gained a lot of experience in playing games and hopefully that will show.”
Drinkwater scored one goal and made three assists in 47 appearances in all competitions last season in what was ultimately a disappointing campaign for Leicester.
The England international is the sixth arrival at Stamford Bridge following Willy Caballero, Antonio Rudiger, Tiemoue Bakayoko, Alvaro Morata and Davide Zappacosta.
Chelsea started the season with a surprise 3-2 loss to Burnley before successive Premier League victories over Tottenham Hotspur and Burnley.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news