In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the effects of frequency dispersion, magneto-electric coupling, and spatial dispersion, even in frequency band-gaps or when the materials are lossy. We formulate a homogenization problem to characterize a generic microstructured artificial material, and demonstrate that it is equivalent to an integral-differential system. We prove that this complex system can be reduced to a standard integral equation and solved using standard methods. To illustrate the application of the proposed method, we homogenize several important metamaterial configurations involving split ring resonators and metallic wires.