A mismatch of atomic registries between single-layer transition metal dichalcogenides (TMDs) in a two-dimensional (2D) van der Waals heterostructure produces a moire superlattice with a periodic potential, which can be fine-tuned by introducing a twist angle between the materials. This approach is promising both for controlling the interactions between the TMDs and for engineering their electronic band structures, yet direct observation of the changes to the electronic structure introduced with varying twist angle has so far been missing. Here, we probe heterobilayers comprised of single-layer MoS2 and WS2 with twist angles ranging from 2 degrees to 20 degrees and determine the twist angle-dependent evolution of the electronic band structure using micro-focused angle-resolved photoemission spectroscopy. We find strong interlayer hybridization between MoS2 and WS2 electronic states at the (Gamma) over bar -point of the Brillouin zone, leading to a shift of the valence band maximum in the heterostructure. Replicas of the hybridized states are observed at the center of twist angle-dependent moire mini Brillouin zones. We confirm that these replica features arise from the inherent moire potential by comparing our experimental observations with density functional theory calculations of the superlattice dispersion. Our direct visualization of these features underscores the potential of using twisted heterobilayer semiconductors to engineer hybrid electronic states and superlattices that alter the electronic and optical properties of 2D heterostructures for a wide range of twist angles.