Energy levels of a polaron bound indirectly to impurity ions in a double quantum well system are calculated in the adiabatic approximation by means of a perturbation method, in which the unperturbed system is treated by the variational theory of Lee- Low-Pines. The polaron binding energy as well as impurity energy levels are studied for variable well width, barrier thickness and magnetic fields. It is shown that the electron-phonon interaction contributes greatly to the binding energy and must not be ignored in a system of double quantum wells in any case.