Demands on high-quality two-dimensional (2D) chalcogenide thin films are growing due to the findings of exotic physical properties and promising potentials for device applications. However, the difficulties in controlling epitaxy with defect density and an unclear understanding of van der Waals epitaxy (vdWE) for 2D chalcogenide film on the substrate have been major obstacles for the further advances of these materials. In this research, we demonstrate new scalable approaches enabling the vdWE of 2D chalcogenide films on 2D and 3D substrates. As a proof of concept, highly-crystalline bismuth antimony telluride thermoelectric thin-films were epitaxially grown on 2D (graphene) and 3D (α-Al2O3) substrates by pulsed laser deposition. It was elucidated that the vdWE growth mechanism of these films on 2D and 3D substrates is utterly governed by the surface reaction of the substrate with chalcogen. In particular, this peculiar vdWE renders the high-quality 2D chalcogenide film with superior carrier mobility and low defect density comparable to single crystal. Furthermore, exceptionally low thermal conductivity were observed in these vdWE films.