Two-dimensional (2D) vertically stacked heterostructures based on layered transition-metal dichalcogenides (TMDCs) have remarkable potential in future applications due to their rich interlayer related properties, such as interlayer excitons, tunable interlayer band alignments. However, the controlled growth of TMDC bilayer heterostructures with preferred stacking structure remains challenging. Here, we report a two-step van der Waals epitaxial vapor growth of WSe2/WS2 vertically stacked bilayer heterostructures with controllable commensurate crystallographic alignments (so called AA and AB stacking), by controlling the deposition temperature. Moire patterns were obtained in both AA and AB stacked WSe2/WS2 heterostructures. The stacking configuration of the vertical heterostructures was verified by the second harmonic generation signals. Photoluminescence and Raman spectroscopy studies further confirm that the heterostructures with different stacking configuration have obviously different optical properties, which is ascribed to the distinct interlayer coupling and resonance excitation between the distinguishing AA and AB stacked heterostructures. The controlled growth of AA and AB stacked heterostructures could provide an importance platform not only for fundamental researches but also for functional electronic and optoelectronic device applications.