The well-known gear tooth defects such as root cracks and flank spalls have been widely investigated in previous studies to model their effects on the time varying mesh stiffness (TVMS) and consequently the dynamic response of motor-gearbox systems. Nevertheless, the effect of assembly errors such as the center distance and the eccentricity has been less considered in past works. Determining the signature of these errors on the system response can help for their early detection and diagnostic to avoid overloading and failure of gears. An original geometric-based method combined with the potential energy method is proposed in this paper to accurately model the effect of these assembly errors on the TVMS of mating spur gear pairs. This is achieved by updating the line of action equation (LOA) at each meshing step using the actual coordinates of gear centers and employing a contact detection algorithm (CDA) to determine the actual contact points coordinates. An electrical model of a three-phase induction machine was then coupled with a dynamic model of a one-stage spur gear system to simulate the effect of assembly errors on the electromechanical response of the motor-gearbox system. The simulation results showed that the center distance error induces a reduction in the TVMS magnitude and the contact ratio, whereas the eccentricity error causes a double modulation of the TVMS magnitude and frequency. In addition, the results showed that assembly errors can be detected and diagnosed by analyzing the system vibration and the motor phase-current.