Carlisle player-manager Paul Simpson told his club's official website: "He's a player that I actually tried to sign in the summer when I heard that he was available, but Bristol City got him. We are delighted to be able to bring him here now as he is a very experienced player who can change any game. We're looking forward to working with him and I know he's looking forward to getting down to business with us."
Bridges, who also played for Sunderland and Newcastle, has found himself out of favour at Bristol City following the arrival of new boss Gary Johnson just four months after he joined the League One side.
He has already been linked with possible loan moves back to his native north east with Darlington or Hartlepool after being told by Johnson he does not figure in his plans following the sacking of former boss Brian Tinnion.