Experimental models of the human brain are needed for basic understanding of its development and disease. Human brain organoids hold unprecedented promise for this purpose; however, they are plagued by high organoid-to-organoid variability. This has raised doubts as to whether developmental processes of the human brain can occur outside the context of embryogenesis with a degree of reproducibility that is comparable to the endogenous tissue. Here we show that an organoid model of the dorsal forebrain can reliably generate a rich diversity of cell types appropriate for the human cerebral cortex. We performed single-cell RNA-sequencing analysis of 166,242 cells isolated from 21 individual organoids, finding that 95% of the organoids generate a virtually indistinguishable compendium of cell types, following similar developmental trajectories and with a degree of organoid-to-organoid variability comparable to that of individual endogenous brains. Furthermore, organoids derived from different stem cell lines show consistent reproducibility in the cell types produced. The data demonstrate that reproducible development of the complex cellular diversity of the central nervous system does not require the context of the embryo, and that establishment of terminal cell identity is a highly constrained process that can emerge from diverse stem cell origins and growth environments.