The 28-year-old joins from Russian side Dynamo Moscow until the end of the season and is eligible to play in the Champions League knockout stages.
Jose Mourinho said: "We have Essien suspended and injured and we lose Geremi to the African Nations Cup. He is also a solution in midfield."
Maniche said: "I have had offers from other big European teams but once Chelsea became interested there was only one team.
"Mourinho is the key to me signing - he has been after me for some time. He is my maestro. He knows me from my time at Porto and Benfica.
"I would be crazy to turn them down, because of the manager and because I have known some of the players there for years."
Chelsea could make the move permanent in the summer for £5m.