The Ivory Coast striker departs after eight years at Stamford Bridge, during which time he won three Premier League titles, four FA Cups and two League Cups in addition to the Champions League won at the weekend in Munich.
Drogba scored a late equaliser against Bayern Munich at the Allianz Arena which forced extra time in the UEFA showpiece, and netted the decisive penalty in the subsequent shootout to land the West London club a first European Cup triumph.
The 34-year-old's contract expires this summer, and there has been a great deal of speculation that his next move will be to Chinese club Shanghai Shenhua.
Chelsea chief executive Ron Gourlay told the club's official website: "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."
Drogba leaves Chelsea as one of the most pivotal figures in their history. The former Marseille striker, signed for £24 million back in 2004, has scored nine times in as many cup finals for the Blues.
"I wanted to put an end to all the speculation and confirm that I am leaving Chelsea," he told the club's 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.
"As a team we have accomplished so much and have won every single trophy possible. 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 [owner] Roman [Abramovich] 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."