The 34-year-old, who joined the Blues from Marseille eight years ago for £24 million, hit the decisive penalty to win them the Champions League final on Saturday with his last kick for the side.
He revealed that leaving Stamford Bridge was a tough decision to make, but felt that it was the right time to seek other opportunities.
"I wanted to put an end to all the speculation and confirm that I am leaving Chelsea," Drogba told the club's official website. "It has been a very difficult decision for me to make and I am very proud of what we have achieved but the time is right for a new challenge for me.
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"Saturday was a very special moment for everyone at the club and for all the fans, and I am very proud to have played my part in bringing many trophies to this club, which has been my home for the last eight years.
"I would like to take this opportunity to thank everyone at the club especially Roman [Abramovich, owner] and my team-mates, many of whom have become very close friends and will be my friends for life.
"I would also like to say a very special thank you to the Chelsea fans who have shown me so much love and support over the years.
"I wish the club all the best and continued success for the future - you will always be in my heart."
Chelsea chief executive Ron Gourlay praised the impact that the Ivory Coast international has had on the club, stating: "Didier is undoubtedly a Chelsea legend and will always be part of the Chelsea family.
"He is certainly leaving on a high after Saturday night but he feels the time is right for a new challenge.
"Of course Didier has contributed so much to all of Chelsea's recent successes. He has been a consummate professional during his entire time here and as one of the natural leaders in our squad he has been an inspiration to a lot of our younger players.
"We have known for some time that this outcome was likely but Didier and the club only made a final decision on that in the last couple of days, because for obvious reasons neither Didier nor the club wanted to distract focus away from the Champions League final.
"The talks were amicable all the way through and we wish him all the best for the future. He is welcome back to Stamford Bridge at any time - either as a player or as a guest of ours."
|"We have known for some time that this outcome was likely but did not want to distract from the Champions League final"
- Ron Gourlay
Drogba netted 157 times in his 341 appearances for the club, leaving him fourth on Chelsea's all-time scoring chart, with 34 of those goals coming in European competitions.
He also won three Premier League titles, four FA Cups, two League Cups and the Champions League during his spell at Stamford Bridge.