This thesis presents novel feedback and feedforward control system design strategies for active to passive vibration mitigation of residual vibrations on high speed machine tools. Residual vibrations on high-speed machine tools are triggered when the machine axes (table) undergo large accelerations, which induce sudden inertial forces and excite the lightly damped structural modes of the machine tool structure. The proposed active vibration mitigation design approach utilizes an accelerometer, and feed the spindle (tool-tip) acceleration and velocity back to the motion controller to dampen them. On the other hand, the passive vibration mitigation approach shapes the frequency spectrum of reference motion trajectories (commands) to avoid triggering residual vibrations of the feed drive transmission system. Design of the proposed active and passive techniques require accurate modeling of the machine tool’s structural dynamics. Hence, time and frequency domain identification methods are presented. In order to facilitate a practical tuning strategy, a convex-optimization based iterative tuning approach is also presented. The proposed active and passive vibration mitigation design method are tested experimentally and show significant improvements in the performance, command tracking and vibration suppression.