This paper explores the application of a fully actuated system (FAS) approach to a spacecraft rendezvous system with actuator saturation. A FAS model for the spacecraft rendezvous system is developed, followed by the design of an extended state observer (ESO) to estimate unmeasurable states and the system's nonlinear terms. The saturation issue is addressed using the convex hull method. By the designed ESO, a state feedback controller for the system is designed using the FAS approach, resulting in a constant linear closed-loop system whose eigenvalues can be arbitrarily assigned. This method simplifies the controller design process and provides a more accurate system model without the linearisation of nonlinear terms, thereby improving control accuracy. Simulation results show the effectiveness and usefulness of the proposed method.