Gastric and small intestinal organoids differentiated from human pluripotent stem cells (hPSCs) have revolutionized the study of gastrointestinal development and disease. Distal gut tissues such as cecum and colon, however, have proved considerably more challenging to derive in vitro. Here we report the differentiation of human colonic organoids (HCOs) from hPSCs. We found that BMP signaling is required to establish a posterior SATB2+ domain in developing and postnatal intestinal epithelium. Brief activation of BMP signaling is sufficient to activate a posterior HOX code and direct hPSC-derived gut tube cultures into HCOs. In vitro, HCOs express colonic markers and contained colon-specific cell populations. Following transplantation into mice, HCOs undergo morphogenesis and maturation to form tissue that exhibits molecular, cellular, and morphologic properties of human colon. Together these data show BMP-dependent patterning of human hindgut into HCOs, which will be valuable for studying diseases including colitis and colon cancer.