This article proposes an observer-based discrete-time cascaded control (ODCC) strategy for lateral stabilization of Steer-by-Wire (SbW) vehicles with consideration of uncertainties and disturbances. First, for the observation of the sideslip angle and yaw rate, an information fusion-based unscented Kalman filter (IFUKF) is designed to reduce the negative effect from the variation of the parameters; Second, aiming to eliminate the errors of control variables for lateral stabilization of SbW vehicles, a discrete-time sliding mode predictive control (DSMPC) is presented to deal with matched and mismatched uncertainties and input constraint; Third, to reduce the tracking error between the actual front wheel steering angle and the desired one generated by the DSMPC, a combination of discrete-time fast terminal sliding mode and active disturbance rejection control is proposed to tackle the problems of parameter uncertainties and disturbances in the SbW system. Performance evaluations are conducted via both software-in-the-loop and hardware-in-the-loop to examine the availability and practicability of the ODCC strategy.