Water is one of the most abundant molecules in the form of solid ice phase in the different regions of the interstellar medium (ISM). This large abundance cannot be properly explained by using only traditional low temperature gas-phase reactions. Thus, surface chemical reactions are believed to be major synthetic channels for the formation of interstellar water ice. Among the different proposals, hydrogenation of atomic O (i.e., 2H + O → H2O) is a chemically "simple" and plausible reaction toward water formation occurring on the surfaces of interstellar grains. Here, novel theoretical results concerning the formation of water adopting this mechanism on the crystalline (010) Mg2SiO4 surface (a unequivocally identified interstellar silicate) are presented. The investigated reaction aims to simulate the formation of the first water ice layer covering the silicate core of dust grains. Adsorption of the atomic O as a first step of the reaction has been computed, results indicating that a peroxo ( O 2 2 - ) group is formed. The following steps involve the adsorption, diffusion and reaction of two successive H atoms with the adsorbed O atom. Results indicate that H diffusion on the surface has barriers of 4-6 kcal mol-1, while actual formation of OH and H2O present energy barriers of 22-23 kcal mol-1. Kinetic study results show that tunneling is crucial for the occurrence of the reactions and that formation of OH and H2O are the bottlenecks of the overall process. Several astrophysical implications derived from the theoretical results are provided as concluding remarks.