Band offsets between different monolayer transition metal dichalcogenides are expected to efficiently separate charge carriers or rectify charge flow, offering a mechanism for designing atomically thin devices and probing exotic two-dimensional physics. However, developing such large-area heterostructures has been hampered by challenges in synthesis of monolayers and effectively coupling neighboring layers. Here, we demonstrate large-area (>tens of micrometers) heterostructures of CVD-grown WS2 and MoS2 monolayers, where the interlayer interaction is externally tuned from noncoupling to strong coupling. Following this trend, the luminescence spectrum of the heterostructures evolves from an additive line profile where each layer contributes independently to a new profile that is dictated by charge transfer and band normalization between the WS2 and MoS2 layers. These results and findings open up venues to creating new material systems with rich functionalities and novel physical effects.