Interlayer excitons were observed at the heterojunctions in van der Waals heterostructures (vdW HSs). However, it is not known how the excitonic phenomena are affected by the stacking order. Here, we report twist-angle-dependent interlayer excitons in MoSe2/WSe2 vdW HSs based on photoluminescence (PL) and vdW-corrected density functional theory calculations. The PL intensity of the interlayer excitons depends primarily on the twist angle: It is enhanced at coherently stacked angles of 0 degrees and 60 degrees (owing to strong interlayer coupling) but disappears at incoherent intermediate angles. The calculations confirm twist-angle-dependent interlayer coupling: The states at the edges of the valence band exhibit a long tail that stretches over the other layer for coherently stacked angles; however, the states are largely confined in the respective layers for intermediate angles. This interlayer hybridization of the band edge states also correlates with the interlayer separation between MoSe2 and WSe2 layers. Furthermore, the interlayer coupling becomes insignificant, irrespective of twist angles, by the incorporation of a hexagonal boron nitride monolayer between MoSe2 and WSe2.