The autonomy of any airborne, land borne or waterborne vehicle starts with controlling its speed. To achieve cruise speed control, the conventional approach is to use closed-loop feedback control systems that require high precision sensors. Underwater sensors are expensive due to harsh environment and corrosive properties of seawater. In this study, we propose a speed control system for autonomous underwater vehicles (AUVs) that closes the control loop via a feedforward mechanism, eliminating the need for these expensive sensors. The feedforward control is based on the recently developed self-propulsion estimation model which can accurately predict propeller rotation rate for conventional AUV forms. The model is first validated by comparing the predicted resistance and propeller rotation rate of DARPA Suboff with the experimental and numerical results published in the literature. After observing a good match, the feedforward control system is used to ensure that the AUV reaches a predetermined surge speed. Two different underwater vehicles are considered in presenting the results of this study: the DARPA Suboff and the Gavia AUV, which has real time measurements available in the literature. The feedforward control system developed in this study achieves the desired speed with negligible errors. Transient response analysis shows that the computer simulation results are in good agreement with experimental results for the Gavia AUV.