The present disclosure relates to a hydraulic transmission assembly for a ground vehicle comprises a pump unit and a hydraulic motor assembly connected to the pump unit. The pump unit includes a driven shaft configured to operably connect to a motor of the ground vehicle. The hydraulic motor assembly includes a motor housing configured to rotatably mount to a wheel assembly of the ground vehicle. The housing has a central opening. A stationary output shaft has a first end section received in the central opening and a second end section configured to rigidly attach to a frame of the ground vehicle. The output shaft includes at least one internal fluid passage in fluid communication with at least one fluid passage of the pump unit. Pressurization of the hydraulic motor assembly via the pump unit rotates the motor housing relative to the stationary output shaft which, in turn, rotates the wheel assembly in one of a first direction and second direction.