The 27-year-old joined the Blues from French club Nantes in the summer but managed only one minute of action for the Premier League champions.
Djilobodji's signing was confirmed by Bremen - who finished the first half of the Bundesliga campaign in 16th position out of 18 - on Thursday afternoon.
Former Blues boss Jose Mourinho admitted the Senegal defender was signed on a recommendation
But despite Chelsea's defensive lapses this season, neither Mourinho nor his successor Guus Hiddink, the caretaker boss, opted to field Djilobodji in a Premier League game
He becomes the 32nd Chelsea player to have been on loan at some stage this season
Source : PA