Recent studies have proposed that social norms play a key role in motivating human cooperation and in explaining the unique scale and cultural diversity of our prosociality. However, there have been few studies that directly link social norms to the form, development and variation in prosocial behaviour across societies. In a cross-cultural study of eight diverse societies, we provide evidence that (1) the prosocial behaviour of adults is predicted by what other members of their society judge to be the correct social norm, (2) the responsiveness of children to novel social norms develops similarly across societies and (3) societally variable prosocial behaviour develops concurrently with the responsiveness of children to norms in middle childhood. These data support the view that the development of prosocial behaviour is shaped by a psychology for responding to normative information, which itself develops universally across societies.