The Blues paid £35million to sign the midfielder from Leicester in 2017 and reunite Drinkwater with N’Golo Kante, the pair having won the Premier League title together at the King Power Stadium.
However he struggled to find form while injuries and off-pitch incidents impacted his playing time, resulting in several loan moves and his contract expiring this summer.
“My time at Chelsea has come to an end… actually feels really strange writing this,” he posted on Instagram.
“Me, the club and fans are hugely disappointed with the outcome there is no doubt about that. Injuries, how I have been treated, mistakes I have made, issues of the pitch, lack of game time… the list of excuses could be endless but I would not and can not change what’s happened.
“I’m going to look at positives over the past five years, I have played with great players, coached by awesome managers, worked with some brilliant staff, met some fantastic people, lived in some beautiful places, travelled the world and won some more silverware.
“Football’s a fantastic sport but this for both parties was a business move gone wrong, it’s as black and white as that.
“To the Chelsea fans I apologise for how this has turned out I would of loved for u to see me at my best in that shirt doing what I love. All the best.”