The compositional and structural rearrangements at the catalyst surface during chemical reactions are issues of great importance for understanding and modeling the catalytic processes. Low-energy electron microscopy and photoelectron spectromicroscopy studies of the real-space structure and composition of a Au-modified Rh(110) surface during water formation reveal reorganization processes due to Au mass transport triggered by the propagating reaction fronts. The temporal evolution of the surface reaction results in a 'patterned' surface consisting of separated Au-rich and Au-poor phases with different oxygen coverage, Rh surface structure, and reactivity. The experimental results are complemented by ab initio electronic-structure calculations of the O and Au adsorption phases, which demonstrate that the reorganization of the Au adlayer by the propagating reaction fronts is an energetically driven process. Our findings suggest that reaction-induced spatial inhomogeneity in the surface composition and structure is a common feature of metal catalysts modified with adatoms which become mobile under reaction conditions.