This work presents a novel motor-level Nonlinear Model Predictive Control trajectory tracking controller for an over-actuated quadrotor with tilting propellers. The proposed controller directly provides the motor-level commands for both the tilting and the spinning of the propellers. Moreover, it optimally solves the control allocation problem arising from the system’s over-actuation taking into account the physical constraints of the platform. Leveraging a look-ahead strategy combined with the knowledge of the actuation limits, the proposed solution fully exploits the vehicle capabilities and accurately tracks the desired reference. Simulation results show that the solution proposed outperforms a state-of-the-art controller based on Feedback Linearization, in terms of both trajectory tracking and robustness to unmodeled dynamics.