Astrocytes contribute to the development and regulation of the higher-level functions of the brain, the critical targets of evolution. However, how astrocytes evolve in primates is unsettled. Here, we obtain human, chimpanzee, and macaque induced pluripotent stem-cell-derived astrocytes (iAstrocytes). Human iAstrocytes are bigger and more complex than the non-human primate iAstrocytes. We identify new loci contributing to the increased human astrocyte. We show that genes and pathways implicated in long-range intercellular signaling are activated in the human iAstrocytes and partake in controlling iAstrocyte complexity. Genes downregulated in human iAstrocytes frequently relate to neurological disorders and were decreased in adult brain samples. Through regulome analysis and machine learning, we uncover that functional activation of enhancers coincides with a previously unappreciated, pervasive gain of "stripe" transcription factor binding sites. Altogether, we reveal the transcriptomic signature of primate astrocyte evolution and a mechanism driving the acquisition of the regulatory potential of enhancers.