The Blues beat Bayern Munich 4-3 in a penalty shoot-out after the final at the Allianz Arena had finished 1-1 after extra-time.
Drogba said of his team-mates: "They never give up until the end. This team is amazing."
The Ivory Coast international added of the victory on ITV: "It was written, I think, a long time ago.
"I want to dedicate this cup to all the managers we've had before, all the players I've played with before."
"When we have this guy in goal you have to believe," Drogba said.