Proactive, that is, unsolicited, prosociality is a key component of our hyper-cooperation, which in turn has enabled the emergence of various uniquely human traits, including complex cognition, morality and cumulative culture and technology. However, the evolutionary foundation of the human prosocial sentiment remains poorly understood, largely because primate data from numerous, often incommensurable testing paradigms do not provide an adequate basis for formal tests of the various functional hypotheses. We therefore present the results of standardized prosociality experiments in 24 groups of 15 primate species, including humans. Extensive allomaternal care is by far the best predictor of interspecific variation in proactive prosociality. Proactive prosocial motivations therefore systematically arise whenever selection favours the evolution of cooperative breeding. Because the human data fit this general primate pattern, the adoption of cooperative breeding by our hominin ancestors also provides the most parsimonious explanation for the origin of human hyper-cooperation.