CO hydrogenation and oxidation were conducted over Ir supported on TiO2 and ZrO2 catalysts using a feed mimicking the water–gas shift reformate stream. The influence of the support interaction with Ir and the catalysts’ redox and CO chemisorption properties on activity and selectivity were evaluated. Both catalysts oxidised CO to CO2 in the absence of H2, and a conversion of 70% was obtained at 200 °C. For the CO oxidation in the presence of H2 over these catalysts, the oxidation of H2 was favoured over CO due to H2 spillover occurring at the active metal and support interface, resulting in the formation of interstitials catalysed by Ir. However, both catalysts showed promising activity for CO hydrogenation. Ir-ZrO2 was more active, giving 99.9% CO conversions from 350 to 370 °C, with high selectivity towards CH4 using minimal H2 from the feed. Furthermore, results for the Ir-ZrO2 catalyst showed that the superior activity compared to the Ir-TiO2 catalyst was mainly due to the reducibility of the support and its interaction with the active metal. Controlling the isoelectric point during the synthesis allowed for a stronger interaction between Ir and the ZrO2 support, which resulted in higher catalytic activity due to better metal dispersions, and higher CO chemisorption capacities than obtained for the Ir-TiO2 catalyst.