Gallium phosphide is a low-loss, high-refractive-index semiconductor considered as a promising material for active and passive components in modern nanophotonics. In this work, we show that nanoscale epitaxial layers of GaP with high optical quality can be formed directly on the transparent sapphire wafers despite the symmetry and lattice constant mismatch. This is achieved using a two-step growth technique through the framework of a domain matching epitaxy mechanism. Direct molecular beam epitaxial growth enables the control of material properties and layer thickness with subnanometer precision and allows us to obtain (111)-oriented epitaxial layers of GaP on high-optical-contrast sapphire wafers without the use of postgrowth layer transfer techniques. The influence of growth conditions on the structural quality of GaP-on-sapphire is revealed using Raman spectroscopy and X-ray diffraction reciprocal space mapping. We study the impact of the growth procedure employing a low-temperature seeding layer on the GaP layer morphology and structural quality. Spectroscopic ellipsometry measurements confirm that both the refractive index and the absorption coefficient of the epitaxial GaP layers are close to those of bulk GaP crystals. We also discuss how the GaP layer morphology and structural quality affect its optical density, drawing special attention to the mechanisms of optical losses. Finally, by nanostructuring the grown layer, we fabricate single GaP nanoantennas and confirm their highly resonant optical response in the visible spectral range, thus confirming the feasibility of the reported technology for various nanophotonic applications.