We report on the van der Waals epitaxy of high-quality single-crystalline AlN and the demonstration of AlGaN tunnel junction deep-ultraviolet light-emitting diodes directly on graphene, which were achieved by using plasma-assisted molecular beam epitaxy. It is observed that the substrate/template beneath graphene plays a critical role in governing the initial AlN nucleation. In situ reflection high energy electron diffraction and detailed scanning transmission electron microscopy studies confirm the epitaxial registry of the AlN epilayer with the underlying template. Detailed studies further suggest that the large-scale parallel epitaxial relationship for the AlN epilayer grown on graphene with the underlying template is driven by the strong surface electrostatic potential of AlN. The realization of high-quality AlN by van der Waals epitaxy is further confirmed through the demonstration of AlGaN deep-ultraviolet light-emitting diodes operating at ∼260 nm, which exhibit a maximum external quantum efficiency of 4% for an unpackaged device. This work provides a viable path for the van der Waals epitaxy of ultra-wide bandgap semiconductors, providing a path to achieve high performance deep-ultraviolet photonic and optoelectronic devices that were previously difficult.