Heteroepitaxial iridium thin films were deposited on (0001) sapphire substrates by means of molecular beam epitaxy, and subsequently, one monolayer of graphene was synthesized by chemical vapor deposition. The influence of the growth parameters on the quality of the Ir films, as well as of graphene, was investigated systematically by means of low energy electron diffraction, x-ray reflectivity, x-ray diffraction, Auger electron spectroscopy, scanning electron microscopy, and atomic force microscopy. Our study reveals (111) oriented iridium films with high crystalline quality and extremely low surface roughness, on which the formation of large-area epitaxial graphene is achieved. The presence of defects, like dislocations, twins, and 30° rotated domains in the iridium films is also discussed. The coverage of graphene was found to be influenced by the presence of 30° rotated domains in the Ir films. Low iridium deposition rates suppress these rotated domains and an almost complete coverage of graphene was obtained. This synthesis route yields inexpensive, air-stable, and large-area graphene with a well-defined orientation, making it accessible to a wider community of researchers for numerous experiments or applications, including those which use destructive analysis techniques or irreversible processes. Moreover, this approach can be used to tune the structural quality of graphene, allowing a systematic study of the influence of defects in various processes like intercalation below graphene.