Mapping the origin of human cognitive traits typically relies on comparing behavioral or neuroanatomical features in human phylogeny. However, such studies rely on inferences from comparative relationships and do not incorporate neurogenetic information, as these approaches are restricted to experimentally accessible species. Here, we fused evolutionary genomics with human functional neuroanatomy to reconstruct the neurogenetic evolution of human brain functions more directly and comprehensively. Projecting genome-wide selection pressure (dN/dS ratios) in sets of chronologically ordered mammalian species onto the human brain reference space unmasked spatial patterns of cumulative neurogenetic selection and co-evolving brain networks from task-evoked functional MRI and functional neuroanatomy. Importantly, this evolutionary atlas allowed imputing functional features to archaic brains from extinct hominin genomes. These data suggest accelerated neurogenetic selection for language and verbal communication across all hominin lineages. In addition, the predictions identified strategic thought and decision making as the dominant traits that may have separated anatomically modern humans (AMH) from archaic hominins.