Organogenesis generates higher-order structures containing functional subunits, connective components, and progenitor niches. Despite recent advances in organoid-based modeling of tissue development, recapitulating these complex configurations from pluripotent stem cells (PSCs) has remained challenging. In this study, we report assembly of kidney organoids that recapitulate embryonic branching morphogenesis. By studying the distinct origins and developmental processes of the ureteric bud, which contains epithelial kidney progenitors that undergo branching morphogenesis and thereby plays a central role in orchestrating organ geometry, and neighboring mesenchymal nephron progenitors, we established a protocol for differential induction of each lineage from mouse and human PSCs. Importantly, reassembled organoids developed the inherent architectures of the embryonic kidney, including the peripheral progenitor niche and internally differentiated nephrons that were interconnected by a ramified ureteric epithelium. This selective induction and reassembly strategy will be a powerful approach to recapitulate organotypic architecture in PSC-derived organoids.