Graphene transfer methods either employ support layers that have to be removed after transfer, giving rise to impurities, or are based on delamination from bulk crystals, yielding only small flakes with various thicknesses. We present a graphene transfer method overcoming these disadvantages and working under ultrahigh vacuum. It is based on wafer bonding and uses a Teflon-supported graphene bilayer as a source. We demonstrate transfer of one graphene monolayer onto atomically clean Ir(111) and Cu(100) single-crystal surfaces over 5 × 5 mm2 large areas. Auger electron spectroscopy reveals that 70–100% of a graphene monolayer is transferred and that this layer is free from chemical defects, even within the detection limit of synchrotron-based X-ray absorption spectroscopy. Raman and X-ray absorption spectroscopy evidence high structural quality of the transferred graphene, and scanning tunneling microscopy shows the same moiré structure of graphene on Ir(111) that is obtained for chemical vapor deposition on that substrate. We show the versatility of our approach by creating a graphene bilayer on Ir(111). Our method enables us to cap entire surfaces in ultrahigh vacuum with a monolayer of clean 2D material, either for sealing them from the environment or for the creation of novel 3D metamaterials by sequential epitaxial growth and graphene transfer.