The ion-beam synthesis of Ga2O3 nanocrystals in dielectric matrices on silicon is a novel and promising way for creating nanomaterials based on gallium oxide. This research studies the regularities of changes, depending on the synthesis regimes used, in the chemical composition of ion-implanted SiO2/Si and Al2O3/Si samples. It has been shown that the formation of Ga-O chemical bonds occurs even in the absence of thermal annealing. We also found the conditions of ion irradiation and annealing at which the content of oxidized gallium in the stochiometric state of Ga2O3 exceeds 90%. For this structure, the formation of Ga2O3 nanocrystalline inclusions was confirmed by transmission electron microscopy.