Drogba who left Chelsea in 2012 after scoring the last penalty that won them the Champions League,agreed a one-year deal to return to the club.
Drogba told Chelsea's official site: "It was an easy decision - I couldn't turn down the opportunity to work with Jose again."
"Everyone knows the special relationship I have with this club and it has always felt like home to me.
"My desire to win is still the same and I look forward to the opportunity to help this team. I am excited for this next chapter of my career."
Jose Mourinho earlier on Friday hinted that Drogba will be returning to the club,but also pointed out that he will be a squad player.
After Drogba's arrival was confirmed,Mourinho said of the signing: "He's coming because he's one of the best strikers in Europe.
"I know his personality very well and I know if he comes back he's not protected by history or what he's done for this club previously. He is coming with the mentality to make more history."