The 36-year-old striker and fans favourite returns to Stamford Bridge after leaving in 2012 for spells at Shanghai Shenhua and Galatasaray.
"It was an easy decision - I couldn't turn down the opportunity to work with Jose again," Drogba said.
"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.
Mourinho added: "He is coming with the mentality to make more history."