Size-selected subnanometer cobalt clusters with 4, 7, and 27 cobalt atoms supported on amorphous alumina and ultrananocrystalline diamond (UNCD) surfaces were oxidized after exposure to ambient air. Grazing incidence X-ray absorption near-edge spectroscopy (GIXANES) and near-edge X-ray absorption fine structure (NEXAFS) were used to characterize the clusters revealed a strong dependency of the oxidation state and structure of the clusters on the surface. A dominant Co2+ phase was identified in all samples. However, XANES analysis of cobalt clusters on UNCD showed that similar to 10% fraction of a Co-0 phase was identified for all three cluster sizes and about 30 and 12% fraction of a Co3+ phase in 4, 7, and 27 atom clusters, respectively. In the alumina-supported clusters, the dominating Co2+ component was attributed to a cobalt aluminate, indicative of a very strong binding to the support. NEXAFS showed that in addition to strong binding of the dusters to alumina, their structure to a great extent follows the tetrahedral morphology of the support. All supported clusters were found to be resistant to agglomeration when exposed to reactive gases at elevated temperatures and atmospheric pressure.