There is also an option to buy the striker at the end of next season if he impresses at Stamford Bridge.
'I am very happy to be joining Chelsea and can't wait to start training and help with our aim of retaining the league title and being successful in Europe,' Falcao said.
Manchester United turned down the chance to sign Falcao on a permanent deal, or to extend his loan, and this made Mourinho to make his move and boost his strikeforce following the departure of Didier Drogba.
Chelsea youngster Mario Pasalic moved in the opposite side as part of the agreement.
