A method for the formation of gradient index tapered optical waveguides with predicted shape is proposed and described analytically. The method is applicable for structures fabricated by electric-field assisted ion-exchange in glass. The technique is based on the control of the taper shape by applying a non-uniform electrical field during the waveguide formation process. For experimental verification optical waveguides with tapers were formed by electrically induced migration of K + ions. An optical coupler based on such a tapered waveguide has demonstrated 1.2° outcoupled beam divergence. The method proposed can be used to form different integrated optical elements, e.g. mode filters, horn structures etc.