Foundation system for towers, especially for onshore wind turbines, comprising a central shaft buried or partially buried, preferably hollow and formed by dowels made from precast concrete, an essentially flat lower slab and completely buried, and lateral support means in the form of inclined struts that are joined at their upper end with the central shaft and at its lower end with the lower slab, and that are preferably entirely buried. The wind tower is located on the partly buried main shaft. The foundation system may comprise other lower elements connected with the lower slab, such as radial ribs or peripheral beams. The struts are preferably prefabricated elements incorporating an efficient and economical connection system by pre-stressing. The foundation system maximizes the fraction of the weight of the foundation by gravity generated by soil or ballast material, allowing an important economy in the structural materials of the foundation.