Electrodynamic tethered satellites with low thrust-to-weight ratios can only perform orbital transfers over a large number of revolutions, which poses a real challenge to short time scale optimal control. An approach to multi-revolution, large-time-scale optimal control of electrodynamic tethered satellites is investigated in this paper using an orbital averaging technique based on Fourier series expansion. The control profile is transformed in Fourier space and the secular dynamics equations in arbitrary elliptic orbits are represented as functions of thrust Fourier coefficients. With direct collocation, the optimal control problem based on Fourier series expansion is converted to a parameter optimization problem that can be solved by sequence quadratic planning. This method can determine the optimal control solutions accurately and reduce the computational requirements significantly. Numerical examples of maximum climb transfer and minimum time orbit change are presented to demonstrate the validity of the proposed approach.