A novel approach combining the moment method (MoM) and the discrete Fourier transform (DFT) is developed for the fast analysis of electromagnetic (EM) radiation/scattering from electrically large, finite, planar rectangular arrays. In particular, the unknown array distribution to be solved is represented in terms of the DFT within the MoM for a given array excitation. The proposed DFT-MoM approach for large arrays has the advantage that it can overcome the inefficiency of the conventional MoM approach by drastically reducing the number of unknowns. The latter is possible because only a relatively few DFT terms are significant in this DFT-MoM. A useful criterion to select significant DFT terms is described. Numerical results are presented to indicate the efficiency and accuracy of the DFT-MoM analysis for determining the array distribution and the radiation pattern of large rectangular arrays with uniform excitation. It is found that the efficiency and accuracy of the DFT-MoM increases dramatically with an increase in array size. Furthermore, the DFT representation employed within the MoM can provide an asymptotic closed form solution for both the near and far fields of the array, which can be described in the ray format of the uniform geometrical theory of diffraction (UTD).