Drogba, 34, joined Chelsea from Olympique Marseille [ Images ] in 2004 and scored 157 goals in 341 appearances for the club.
"I wanted to put an end to all the speculation and confirm that I am leaving Chelsea," Drogba said on the club website (www.chelseafc.com).
"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."
Drogba enjoyed a glittering eight years in the Premier League in which he won three league titles, four FA Cups and two League Cups.
He capped his trophy-laden career at the West London [ Images ] club by starring in their Champions League [ Images ] final victory over Bayern Munich [ Images ] on Saturday, when he scored a late equaliser before netting the decisive penalty in the shootout.
"Didier is undoubtedly a Chelsea legend and will always be part of the Chelsea family," Chelsea chief executive Ron Gourlay said.
"He is certainly leaving on a high after Saturday night but he feels the time is right for a new challenge.
"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 [ Images ] at any time - either as a player or as a guest of ours."
Drogba has been linked with a move to Chinese club Shanghai Shenhua where he would join up with former Chelsea team mate Nicolas Anelka [ Images ] who left Stamford Bridge in January.