Modern genetic studies indicate that human brain evolution is driven primarily by changes in gene regulation, which requires understanding the biological function of largely non-coding gene regulatory elements, many of which act in tissue specific manner. We leverage chromatin interaction profiles in human fetal and adult cortex to assign three classes of human-evolved elements to putative target genes. We find that human-evolved elements involving DNA sequence changes and those involving epigenetic changes are associated with human-specific gene regulation via effects on different classes of genes representing distinct biological pathways. However, both types of human-evolved elements converge on specific cell types and laminae involved in cerebral cortical expansion. Moreover, human evolved elements interact with neurodevelopmental disease risk genes, and genes with a high level of evolutionary constraint, highlighting a relationship between brain evolution and vulnerability to disorders affecting cognition and behavior. These results provide novel insights into gene regulatory mechanisms driving the evolution of human cognition and mechanisms of vulnerability to neuropsychiatric conditions.