This article presents a computationally efficient and high performing approximate long-horizon model predictive control (MPC) for permanent magnet synchronous motors (PMSMs). Two continuous control set MPC (CCS-MPC) formulations are considered: the classical current tracking delta MPC (Del-MPC) and the torque tracking economic MPC (EMPC). To achieve offset-free torque tracking under model uncertainties and in all regions of operation, a disturbance observer and a dq -current reference generator are used. To enable real-time implementation of the long-horizon CCS-MPC, the development of a real-time capable solver is not required, since MPC approximation based on deep neural networks (DNNs) is considered and utilized for controller’s evaluation at run time. The approximation is done by training the DNN to learn the MPC functionality based on offline-generated training data and in an open-loop manner. The robust and offset-free tracking performance of the proposed DNN-based approximate long-horizon Del-MPC and EMPC has been validated through simulation and real-time implementation at test bench and compared to the state-of-the-art field oriented control (FOC) using internal model controller with field-weakening (FW) part and to the exact short-horizon MPC based on the fast gradient method (FGM-MPC). Results show that the long-horizon MPC can achieve significantly faster torque transient responses in comparison with the short-horizon FGM-MPC and the conventional FOC, especially in FW region.