The human brain has undergone rapid expansion since humans diverged from other great apes, but the mechanism of this human-specific enlargement is still unknown. Here, we use cerebral organoids derived from human, gorilla, and chimpanzee cells to study developmental mechanisms driving evolutionary brain expansion. We find that neuroepithelial differentiation is a protracted process in apes, involving a previously unrecognized transition state characterized by a change in cell shape. Furthermore, we show that human organoids are larger due to a delay in this transition, associated with differences in interkinetic nuclear migration and cell cycle length. Comparative RNA sequencing (RNA-seq) reveals differences in expression dynamics of cell morphogenesis factors, including ZEB2, a known epithelial-mesenchymal transition regulator. We show that ZEB2 promotes neuroepithelial transition, and its manipulation and downstream signaling leads to acquisition of nonhuman ape architecture in the human context and vice versa, establishing an important role for neuroepithelial cell shape in human brain expansion.