A bicycle rear derailleur is basically provided with a base member, a link mechanism, outer and inner plate members, a guide pulley and a tension pulley. At least one of the outer and inner plate members includes a bent portion integrally formed with the at least one of the outer and inner plate members to prevent a chain from disengaging from at least one of the tension pulley and the guide pulley. The bent portion is formed by bending an inner section of the at least one of outer and inner plate members in a direction towards the other of the at least one of the outer and inner plate members. The inner section is spaced inwardly from an external peripheral edge of the at least one of the outer and inner plate members.