This letter presents a design framework and novel control strategy for a compact coaxial magnetic-gear-based actuation module suitable for small-to-mid-sized mechanical and robotic applications. The proposed actuation module adopts a non-contact magnetic coupling mechanism to transmit rotational power with a predetermined gear ratio, in contrast to traditional mechanical gear-based transmissions. This approach offers several advantages such as enhanced backdrivability, hardware safety, and transparency when compared to conventional contact-based transmissions. Furthermore, the magnetic coupling effect provides a spring-like characteristic that can be utilized to implement a series elastic actuation enabling sensorless torque control. The design of the magnetic gear was optimized using a differential evolution method, and a dynamic model was formulated to specify its dynamic characteristics. Finally, a composite disturbance observer-based torque control algorithm was developed, which capitalizes on the features of the magnetic spring. The proposed control algorithm was validated through several experiments.