Heteroepitaxy of semiconductors on two-dimensional (2-d) atomic layered materials enables the use of flexible and transferable inorganic electronic and optoelectronic devices in various applications. Herein, we report the shape- and morphology-controlled van der Waals (vdW) epitaxy of ZnO nanostructures on hexagonal boron nitride (hBN) insulating layers for an architectured semiconductor integration on the 2-d layered materials. The vdW surface feature of the 2-d nanomaterials, because of the surface free of dangling bonds, typically results in low-density random nucleation-growth in the vdW epitaxy. The difficulty in controlling the nucleation sites was resolved by artificially formed atomic ledges prepared on hBN substrates, which promoted the preferential vdW nucleation-growth of ZnO specifically along the designed ledges. Electron microscopy revealed crystallographically domain-aligned incommensurate vdW heteroepitaxial relationships, even though ZnO/hBN is highly lattice-mismatched. First-principles theoretical calculations confirmed the weakly bound, noncovalent binding feature of the ZnO/hBN heterostructure. Electrical characterizations of the ZnO nanowall networks grown on hBN revealed the excellent electrical insulation properties of hBN substrates. An ultraviolet photoconductor device using the vdW epitaxial ZnO nanowall networks/hBN heterostructure was further demonstrated as an example of hBN substrate-based device applications. The architectured heteroepitaxy of semiconductors on hBN is thus expected to create many other device arrays that can be integrated on a piece of substrate with good electrical insulation for use in individual device operation.