The 36-year-old left Chelsea in 2012 after scoring the winning penalty in the Champions League final against Bayern Munich. Drogba has since played for Shanghai Shenhua and Galatasaray.
The striker has scored a Chelsea-record 34 goals in European competition, including nine in nine cup finals.
Drogba on his return, via ChelseaFC.com:
"It was an easy decision - I couldn't turn down the opportunity to work with (manager) Jose (Mourinho) 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."
The Ivory Coast international started one game and was subbed in twice at the 2014 FIFA World Cup, where Ivory Coast was eliminated during the group stage. He has 104 total caps and 64 goals scored for his country.
Drogba joined Chelsea from Marseille in July 2004 and won three Premier League titles, four FA Cups, two League Cups and a Champions League with the Blues.
The financial terms of the deal were not announced.
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