Electron-ion recombination observed in storage ring experiments shows a strong enhancement relative to what standard radiative recombination rates predict. We simulate the effect of a transient motional electric field induced by the merging of an electron and an ion beam in the electron cooler which opens an additional pathway for free-bound transitions of electrons. We show that the measured rate contains a significant contribution from radiative stabilization of Rydberg states formed by this transient motional electric field. The absolute excess recombination rates obtained are in good agreement with the experimental data. The scaling of the rate with the ion charge and the magnetic guiding field is analyzed.