Rh(III) complexes [Rh(H)(X)(κ 2 -NSi tBu2OPy )(L)] (X = Cl, L = PCy 3 , 2a; PH t Bu 2 , 2b; X = OTf, L = PCy 3 , 3a; PH t Bu 2 , 3b) (NSi tBu2OPy = 4-methylpyridin-2yloxy-ditertbutylsilyl) have been prepared and characterized by means of elemental analysis and nuclear magnetic resonance (NMR) spectroscopy. The solid-state structures of complexes 2a, 2b, and 3a have been determined by X-ray diffraction studies. Computational analyses of the bonding situation of these species evidence the electron-sharing nature of the Rh−Si bond and the significant role of the electrostatic component in the interaction between the transition metal fragment [Rh(H)(PR 3 )-(X)] • and the [NSi tBu2OPy ] • ligand. In addition, a comparative study of the activity of 2a, 2b, 3a, 3b, and related iridium species as catalysts for the hydrogenation of olefins has been performed. The best catalytic results have been obtained when using the Rh(III) species 3a, with triflate and PCy 3 ligands, as catalyst. Computational density functional theory studies show that the formation of the alkane is thermodynamically favored and that the rate-limiting step corresponds to the hydrogen activation, which takes place via a σ-complex-assisted metathesis mechanism.