The copper–ceria (CuOx/CeO2) system has been extensively investigated in several catalytic processes, given its distinctive properties and considerable low cost compared to noble metal-based catalysts. The fine-tuning of key parameters, e.g., the particle size and shape of individual counterparts, can significantly affect the physicochemical properties and subsequently the catalytic performance of the binary oxide. To this end, the present work focuses on the morphology effects of ceria nanoparticles, i.e., nanopolyhedra (P), nanocubes (C), and nanorods (R), on the water–gas shift (WGS) performance of CuOx/CeO2 catalysts. Various characterization techniques were employed to unveil the effect of shape on the structural, redox and surface properties. According to the acquired results, the support morphology affects to a different extent the reducibility and mobility of oxygen species, following the trend: R > P > C. This consequently influences copper–ceria interactions and the stabilization of partially reduced copper species (Cu+) through the Cu2+/Cu+ and Ce4+/Ce3+ redox cycles. Regarding the WGS performance, bare ceria supports exhibit no activity, while the addition of copper to the different ceria nanostructures alters significantly this behaviour. The CuOx/CeO2 sample of rod-like morphology demonstrates the best catalytic activity and stability, approaching the thermodynamic equilibrium conversion at 350 °C. The greater abundance in loosely bound oxygen species, oxygen vacancies and highly dispersed Cu+ species can be mainly accounted for its superior catalytic performance.