The limited availability of vehicle state information, including tire-road forces and vehicle velocities, restricts the development of control strategies for intelligent vehicles and new energy vehicles. This study proposes a modular estimation scheme for tire-road forces and vehicle velocities that can effectively cope with the cyclic coupling of the vehicle dynamics. The longitudinal tire-road forces are estimated using a sliding mode observer. Then, an observer for the lateral tire-road forces that exist in a cascade structure with the longitudinal tire-road force observer is designed. Non-linear vehicle velocity observers that take the estimated longitudinal and lateral tire-road forces as inputs are designed. A genetic algorithm approach is employed to select the observer gains. Finally, experimental validations under normal conditions and offline simulations under critical conditions for verifying the robustness with respect to measurement noise are conducted. The results demonstrate that the proposed modular scheme for tire-road force and vehicle velocity estimation yields acceptable results and has potential value for real vehicle applications.