Finite element simulations of ion transfer (IT) reactions at the nanopipet-supported interface between two immiscible electrolyte solutions (ITIES) were carried out, and the numerical results were generalized in the form of an analytical approximation. The developed theory is the basis of a new approach to kinetic analysis of steady-state voltammograms of rapid IT reactions. Unlike the conventional voltammetric protocol, our approach requires the initial addition of a transferable ion to both liquid phases, i.e., to the filling solution inside a nanopipet and the external solution. The resulting steady-state IT voltammogram comprises two waves corresponding to the ingress of the common ion into the pipet and its egress into the external solution. We demonstrate that both ingress and egress waves are required for characterization of pipet geometry and precise determination of thermodynamic and kinetic parameters for rapid IT reactions. In this way, one can eliminate large uncertainties in kinetic parameters, which are inherent in the previously reported approaches to analysis of nearly reversible steady-state voltammograms of either IT at pipet-supported ITIES or electron transfer at solid electrodes. Numerical simulations also suggest that higher current density at the edge of the nanoscale ITIES increases the significance of electrostatic effects exerted by the charged inner surface of a pipet on IT processes.