Low thrust propulsion systems offer a fuel-efficient means to maneuver satellites to new orbits, however they can only perform such maneuvers when they are continuously operated for a long time. Such long-term maneuvers occur over many orbital revolutions often rendering short time scale trajectory optimization methods ineffective. An approach to long time scale, multirevolution optimal control of an electrodynamic tether is investigated for a tethered satellite system in Low Earth Orbit with atmospheric drag. Optimal control problems are constructed in such a way as to maneuver the satellite to new orbits while minimizing a cost function subject to the constraints of the time-averaged equations of motion by controlling current in the tether. The method of averaging is employed to transform the optimal control problem from the time domain into a Fourier space where the complex problem is drastically reduced to a Zermelo type problem that is solved using a pseudospectral method. Optimal control solutions are determined that maneuver an electrodynamic tether to new orbits over long time scales while managing librational motion using only current in a wire. Results are simulated using a higher fidelity "truth" model to validate the controller performance.