The constrained control of unmanned aerial vehicles (UAVs) is a challenging task due to their nonlinear and underactuacted dynamics. This brief focuses on the position control of a quadrotor UAV with state and input constraints using an inner-outer loop control structure. The outer loop generates a saturated thrust, and the reference roll and pitch angles, while the inner loop is designed to follow these reference angles using a traditional PID controller. Assuming perfect inner loop tracking, the outer loop nested saturation controller guarantees global asymptotic stability for output regulation and tracking. The effect of nonideal inner loop tracking on closed-loop stability is analyzed. The proposed method is experimentally validated on an indoor quadrotor platform.