Surface alloying is an important technique to change chemical properties. In this study, by employing density functional theory (DFT) calculations, the atomic arrangements and energetics of an extensive set of Au–Rh structures in a confined (2 × 1) surface cell on a Rh(111) substrate are investigated. An ordered surface alloy layer composed of 50% Au and 50% Rh is identified as the energetically favored structure, which corresponds to a configuration proposed previously based on scanning tunneling microscopy (STM) imaging [Óvári et al. PCCP 2016, 18, 25230]. Comparing this surface alloy with another candidate structure in terms of Rh and Au adsorption characteristics, the bonding preference among Rh and Au species is recovered. DFT-based simulated STM images reveal bias-voltage-dependent contrast differences among selected corrugated surface layer structures at various Au coverages. Furthermore, several new experimental results obtained by STM and low energy ion scattering (LEIS) on the thermally induced formation of the ordered Au–Rh surface alloy are also presented in this work. Our calculation approach and results are expected to contribute to the understanding of the formation of metallic surface alloys of various chemical compositions.