We report the valence-to-core resonant inelastic x-ray scattering of EuS measured at the L_{3} edge of Eu. The obtained data reveal two sets of excitations: one set is composed of a hole in the S 3p bands and an electron excited to extended Eu 5d band states, and the other is made up from a hole in the Eu 4f states and an electron in localized Eu 5d states bound to the 4f hole by its Coulomb potential. The delocalized excitations arise from the dipole-allowed 5d→2p emissions, whereas the localized excitations result from the dipole-forbidden (quadrupole-allowed) 4f→2p emissions. Both these emission channels have a comparable intensity thanks to a small number of occupied 5d states (≈0.6) combined with a large number of occupied 4f states (seven). We identify the localized electron-hole pairs with the "magnetic excitons" suggested in the past as an interpretation of the sharp features seen in the optical absorption spectra. Our observations provide a direct experimental evidence of these excitons, which has been missing up to now.