Collecting photons from quantum emitters remains a key limitation in light-matter interaction because conventional lenses collect light only from one direction. Here, we introduce a perfect light collector by inverse-designing a surrounding dielectric structure that encloses the emitter to increase photon-collection efficiency toward unity. Decomposing the device into several refractive interfaces enables emission collection from the full 4π solid angle with adiabatic reshaping into a collimated beam. We experimentally demonstrate, in two dimensions, the ray bending that collimates omnidirectional emission. Our collector transforms current paradigms for highly efficient photon collection from narrowband, cavity-based techniques into experimentally robust, broadband, non-resonant dielectric devices.