This paper presents a simultaneous longitudinal and lateral motion control strategy for a full drive-by-wire autonomous vehicle. A nonlinear model predictive control (NMPC) problem is formulated in which the nonlinear prediction model utilizes a spatial transformation to derive the dynamics of the vehicle about the reference trajectory, which facilitates the acquisition of the tracking errors at varying speeds. A reference speed profile generator is adopted by taking account of the road geometry information, such that the lateral stability is guaranteed and the lane guidance performance is improved. Finally, the nonlinear multi-variable optimization problem is simplified by considering only three motion control efforts, which are strictly confined within a convex set and are readily distributed to the four tires of a full drive-by-wire vehicle. Simulation results demonstrate the capability of the proposed controller to follow the reference trajectory while adjusting the vehicle speed automatically.