The trends of high-speed development, integration, and lightweight design are causing electric drive systems to exhibit increasingly complex vibration characteristics. Consequently, vibration suppression methods that comprehensively consider the electromechanical coupling effects of electric drive systems have become one of the key technologies in enhancing the reliability and stability of electric drive systems. This paper addresses the vibration issues in electric drive systems under the combined action of motor and gear excitation sources. By coupling the electromechanical model of the motor with the bending-torsion-axial coupled dynamics model of the gear transmission system, an electromechanical coupling model of the electric drive system is established. Furthermore, based on the electromechanical coupling model of the electric drive system, vibration issues are suppressed from two aspects: active control of the drive motor and passive structural optimization of the transmission system. For active control of the drive motor, a harmonic current injection method based on electromagnetic torque and motor shaft torque is designed. Using a Resonant active disturbance rejection control (RADRC) controller, steady-state harmonic vibration suppression is achieved, while a transient low-frequency jitter suppression method based on damping correction control reduces transient low-frequency jitter in the electric drive system. For passive structural optimization of the transmission system, a passive structural optimization method for gear macro-geometry parameters is designed using an improved particle swarm algorithm, addressing the vibration issues of the gear transmission system at the source. Finally, to overcome the drawback of single optimization of controller design and structural parameter design leading to a loss of global optimal performance, an integrated optimization design method for structural and control parameters is proposed, further enhancing system performance.