Surface alloying is a straightforward route to control and modify the structure and electronic properties of surfaces. Here, we present a systematic study on the structural and electronic properties of three novel rare earth-based intermetallic compounds, namely, ReAu2 (Re = Tb, Ho, and Er), on Au(111) via directly depositing rare earth metals onto the hot Au(111) surface. Scanning tunneling microscopy/spectroscopy measurements reveal very similar atomic structures and electronic properties, e.g., electronic states and surface work functions, for all these intermetallic compound systems because of the physical and chemical similarities between these rare earth elements. Further, these electronic properties are periodically modulated by the moiré structures caused by the lattice mismatches between ReAu2 and Au(111). These periodically modulated surfaces could serve as templates for the self-assembly of nanostructures. In addition, these two-dimensional rare earth-based intermetallic compounds provide platforms to investigate rare earth-related catalysis, magnetisms, etc. in the lower dimensions.