Based on density functional theory calculations, we model the x-ray absorption spectra of the O K edge and the Ti L_2,3 edge in bulk SrTiO₃. Taking into account excitonic effects by solving the Bethe-Salpeter equation is found to be pivotal for obtaining concurrence with the experimental data with respect to the energetic positions and relative intensity of the peaks. Moreover, analysis of the underlying interband transitions in reciprocal space reveals the origin of the prominent peaks and features in the spectra, and provides a deeper understanding of the electronic structure. For example, the characteristic four-peak structure of the Ti L_2,3 edge results from transitions from Ti 2p_3/2 states to the unoccupied Ti 3dt_2g (456.1 eV) and Ti 3de_g states (458.2 eV), followed by transitions from Ti 2p_1/2 states to Ti 3dt_2g (461.8 eV) and Ti 3de_g states (463.7 eV). The first bound exciton is strongly localized in real space, and is confined to essentially one unit cell with 3d_xz character near the Ti sites. On the other hand, the first bound exciton of the O K edge is identified as a charge-transfer type with a dominant contribution from the Ti 3d_xy states hybridized with O p states. Moreover, the spatial distribution of the exciton wave function shows an intriguing two-dimensional spread in the x−y plane, despite the three-dimensional nature of the material.