The structural and electronic properties of MoS2/MoSe2 bilayers are calculated using first-principles methods. It is found that the interlayer van der Waals interaction is not strong enough to form a lattice-matched coherent heterostructure. Instead, a nanometer-scale Moiré pattern structure will be formed. By analyzing the electronic structures of different stacking configurations, we predict that the valence-band maximum (VBM) state will come from the Γ point due to interlayer electronic coupling. This is confirmed by a direct calculation of a Moiré pattern supercell containing 6630 atoms using the linear scaling three-dimensional fragment method. The VBM state is found to be strongly localized, while the conduction band minimum (CBM) state is only weakly localized, and it comes from the MoS2 layer at the K point. We predict such wave function localization can be a general feature for many two-dimensional (2D) van der Waals heterostructures and can have major impacts on the carrier mobility and other electronic and optical properties.