We present a combined theoretical and experimental effort to enable strong light absorption (>70%) in atomically thin MoS2 films (<= 4 layers) for either narrowband incidence with arbitrarily prespecified wavelengths or broadband incidence like solar radiation. This is achieved by integrating the films with resonant photonic structures that are deterministically designed using a unique reverse design approach based on leaky mode coupling. The design starts with identifying the properties of leaky modes necessary for the targeted strong absorption, followed by searching for the geometrical features of nanostructures to support the desired modes. This process is very intuitive and only involves a minimal amount of computation, thanks to the straightforward correlations between optical functionality and leaky modes as well as between leaky modes and the geometrical feature of nanostructures. The result may provide useful guidance for the development of high-performance atomic-scale photonic devices, such as solar cells, modulators, photodetectors, and photocatalysts.