This letter addresses the design of a global saturated trajectory tracking controller for a quadcopter in the presence of external disturbances. The proposed control law guarantees that (i) the thrust force generated by the propellers is bounded with respect to the position and linear velocity errors; (ii) the quadcopter globally converges to a neighborhood of a desired smooth trajectory, achieving global practical stability. Disturbance observers are employed to estimate and compensate for external constant and slowly time-varying disturbances, improving the robustness performance of the controller. A projection operator ensures that the estimates do not wind-up and that they remain within a prescribed bound. To validate the efficiency and robustness of the proposed controller, we present and analyze both simulation and experimental results. The proposed global saturated controller is also compared with a standard backstepping-based trajectory tracking controller to demonstrate the merits and improvements of the proposed controller.