A new approach to the globally stable tracking control of multiple integrators with input saturation and bounded disturbances is proposed. The controller has a hybrid structure. Specifically, in the inner loop, a nonlinear control law is designed in continuous-time domain to have an arbitrarily good disturbance rejection performance at the steady-state while keeping the tracking errors with respect to on-line replanned trajectory within certain positive invariant set even in the presence of input saturation and bounded disturbances, provided that the replanned trajectory satisfies certain conditions. In the outer loop, a trajectory replanning unit implemented in discrete-time domain is constructed to generate a replanned trajectory satisfying those conditions while minimizing the converging time of the replanned trajectory to the desired target. It is theoretically shown that the resulting closed-loop system is globally stable and can track any feasible desired trajectory with a guaranteed steady-state tracking accuracy. Comparative simulation results have been obtained to verify the superior performance of the proposed controller over various existing ones in terms of the disturbance rejection capability and the overall respond speed of the resulting closed-loop system for a third-order integrator chain.