Drogba left Stamford Bridge in the summer of 2012 after scoring the penalty which secured the club's first Champions League triumph against Bayern Munich at the Allianz Arena.
Soon afterwards the Ivorian was voted the greatest player in the club's history in a poll of Chelsea magazine readers, and he received a standing ovation when he returned with Galatasaray for a Champions League tie last season.
Drogba insists he could not turn down the chance to reunite with former boss Jose Mourinho, and says the "special relationship" he enjoys with the club made up his mind.
"It was an easy decision - I couldn't turn down the opportunity to work with Jose again," he told the club's official website. "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."
Mourinho added: "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."