Platinum nanoparticles supported on γ-alumina are widely used as highly dispersed heterogeneous catalysts, in particular in the presence of H2. In the present work, an atomic-scale model for such catalysts is provided, taking into account operating conditions (temperature, hydrogen pressure), thanks to density functional theory calculations coupled to a thermodynamic model. In the absence of hydrogen, Pt13 clusters supported on γ-Al2O3 preferentially lie in a biplanar (BP) morphology in strong interaction with the support’s surface. This structure has a strong affinity towards hydrogen. The increase of hydrogen coverage above 18 H atoms per cluster (H/Pt>1.4) induces a reconstruction from a BP to a cuboctahedral (CUB) morphology as shown by molecular dynamics. This reconstruction is driven by the ability of the CUB structure to adsorb a significant amount of hydrogen with moderate deformation cost. Electronic analyses reveal that a hydride phase is then obtained, with a partial loss of the metallic nature of the Pt13 edifice. Our model is supported by numerous experimental data (temperature-programmed desorption, titration experiments, X-ray absorption spectroscopy). Values higher than 1 for the H/Pt ratio, as measured in previous experimental analyses, are rationalized by the reconstruction process. Moreover, in reaction conditions such as catalytic reforming, the particle remains biplanar with moderate H/Pt ratio and retains its metallic character. The catalytic conditions therefore have a drastic influence on the nature of the catalyst surface.