The Ivory Coast striker will leave when his contract expires at the end of June and is now odds-on to follow his former team-mate Nicolas Anelka to China.
He leaves the club on a high after a starring role in Saturday's Champions League final when he scored an emphatic late headed equaliser before coolly slotting home the decisive penalty in the shootout.
"I wanted to put an end to all the speculation and confirm that I am leaving Chelsea," Drogba said on the club 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."
He found goals easy to get, scoring 157 times in 341 appearances, making him the club's fourth all-time leading scorer, while his 34 European goals are a Chelsea record.
Former manager Andre Villas-Boas tried unsuccessfully to re-invigorate his team by phasing out Chelsea's older players, with Drogba and midfielder Frank Lampard his principal victims.
The departure of Villas-Boas, however, led to a renaissance for Chelsea's 'old guard' who helped to propel the club to a golden finale in which Drogba featured prominently.
"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 at any time - either as a player or as a guest of ours."
