A hydrostatic drive system for a machine is disclosed. The hydrostatic drive system includes a pump, a hydraulic motor configured to receive a pressurized fluid from the pump and a controller operably connected to the pump and the hydraulic motor. The controller is configured to receive an input signal indicative of a current machine speed and a desired machine speed. Further, the controller is configured to output a motor displacement command signal and a pump displacement command signal to adjust a displacement of the hydraulic motor and the pump respectively based on the input signal to maintain at least one of constant machine speed or constant acceleration or constant deceleration during adjustment of the pump displacement and the motor displacement.