The England international completed a last-hour deadline day switch from King Power Stadium to Stamford Bridge after the Blues made their intentions of signing the tough tackling 27-year-old known.
And while many at Leicester were distraught to see Drinkwater depart the club, the Englishman insists he will always cherish his time with the 2015/16 Premier League champions.
“It’s been some journey... Championship, Premier League winners and Champions League quarter-finalists in the space of five years – thank you,” he wrote on social media.
“To the players, staff and the fans... For the medals, the friends, the experiences and most importantly the memories.
“I started as a player at your club... and left as a fan! Good luck.”
Leicester goalkeeper Kasper Schmeichel admitted the Foxes had lost a valuable asset in Drinkwater but wished his former team-mate all the best at Chelsea.
“We are losing one hell of a player, and more importantly one hell of a guy,” said Schmeichel on Twitter.
“All the best Drinky. Some great memories together.”