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"Financially and in a sporting sense I could not refuse Chelsea's offer - I hope I live up to their expectations," said the 26-year-old striker.
Drogba, of the Ivory Coast, will fly to London on Tuesday to sign a four-year contract with the Blues. Drogba said the London club had fought off competition from several Serie A sides to secure his signature.
"I also had offers from Italian clubs, but going to Chelsea is an interesting challenge in my career and I'm glad to join them," he added.
"What convinced me to join Chelsea is that they really showed that they wanted me, and that counts a lot. I will give my best for them now.
"It's very hard to leave Marseille. I've had fantastic times there."
Marseille revealed that Chelsea offered double what Juventus were prepared to pay for Drogba.
And Marseille president Christophe Bouchet said the fee for the striker could be as much as 26.6m.
Didier Drogba became Chelsea's record signing when he completed his transfer from Marseille for a reported 24million.
New Chelsea boss Jose Mourinho has long been an admirer of the Ivory Coast international, and first tried to sign the striker when he was manager at Porto two years ago.