Twisted bilayers of two-dimensional materials have emerged as a highly tunable platform to study and engineer properties of excitons. However, the atomistic description of these properties has remained a significant challenge as a consequence of the large unit cells of the emergent moiré superlattices. To address this problem, we introduce an efficient atomistic quantum-mechanical approach to solve the Bethe–Salpeter equation that exploits the localization of atomic Wannier functions. We then use this approach to study intra- and interlayer excitons in twisted WS2/WSe2 at a range of twist angles. In agreement with experiment, we find that the optical spectrum exhibits three low-energy peaks for twist angles smaller than 2∘. The energy splitting between the peaks is described accurately. We also find two low-energy interlayer excitons with weak oscillator strengths. Our approach opens up new opportunities for the atomistic design of light-matter interactions in ultrathin materials.