Soft actuators with a function of variable stiffness are beneficial to the improvement of the adaptability of robots, expanding the application areas and environments. We propose a tendon-driven soft bending actuator that can change its stiffness using fiber jamming. The actuator is made of an elastomer tube filled with different types of fiber. The three types of fibers play different roles in maintaining the structure, variable stiffness by jamming, and fiber-optic shape sensing while sharing the same structure and materials, realizing a compact form factor of the entire structure. The stiffness of the actuator can be increased to more than three times its original stiffness by jamming. In addition to jamming, the proposed actuator has a special function of shape sensing that estimates the tip location of the actuator based on image sensing from optical fibers packaged with the jamming fibers. The tip position sensing shows the estimation accuracies with the errors of 3.1%, 3.0%, and 6.7% for the x, y, and z axes, respectively, using feature extraction and a deep neural network. The proposed actuator has two degrees of freedom (i.e., bending on two orthogonal planes) and is controlled by two tendons. When connected in series, multiple actuators form a soft robotic manipulator (i.e., arm), physically compliant or capable of delivering a relatively high force to the target objects.