Extensive first principles calculations are carried out to investigate Au monomers and dimers supported on α-Fe2O3(0001) surfaces in terms of structure optimizations, electronic structure analyses, and ab initio thermodynamics calculations of surface phase diagrams. All computations rely on density functional theory in the generalized gradient approximation (Perdew-Burke-Ernzerhof (PBE)) and account for on-site Coulomb interactions via inclusion of a Hubbard correction (PBE+U). The relative stability of Au monomers/dimers on the stoichiometric termination of α-Fe2O3(0001) decorated with various vacancies (multiple oxygen vacancies, iron vacancy, and mixed iron-oxygen vacancies) has been computed as a function of the oxygen chemical potential. The charge rearrangement induced by Au at the oxide contact is analyzed in detail and discussed. On one hand, ab initio thermodynamics predicts that under O-rich conditions, structures obtained by replacing a surface Fe atom with a Au atom are thermodynamically stable over a wide range of temperatures. On the other hand, the complex of a CO molecule on a Au atom substituting surface Fe atoms is thermodynamically stable only in a much more narrow range of values of the O chemical potential under O-rich conditions. In the case of a Au dimer, under O-rich conditions, supported Au atoms at an O-Fe di-vacancy are more stable. However, upon CO adsorption, the complex of a CO molecule and 2 Au atoms located at a single Fe vacancy is more favorable.