In-depth understanding of interfacial atomistic structures is required to design heterointerfaces with controlled functionalities. Using density functional theory calculations, we investigate the interfacial structure of (001) SrTiO3 | (001) MgO, and characterize the stable interface structure. Among the four types of possible interface structures, we show that the TiO2-terminated SrTiO3 containing electrostatically attractive Mg-O and Ti-O ion-ion interactions forms the most stable interface. We also show that oxygen vacancies can be preferentially stabilized across the interface via manipulating interfacial strain. We elucidate that oxygen vacancies are most stable in the tensile-strain material, and unstable in compressive strain material. This stability is explained from equation-of-state analysis using a single crystal, where the oxygen vacancy shows a larger volume than the oxygen ion, thus explaining its stability under tensile-strained conditions.