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Abstract Organoids are lumen‐containing multicellular structures that recapitulate key features of the organs, and are increasingly used in models of disease, drug testing, and regenerative medicine. Recent work has used 3D culture models to form organoids from human induced pluripotent stem cells (hiPSCs) in reconstituted basement membrane (rBM) matrices. However, rBM matrices offer little control over the microenvironment. More generally, the role of matrix viscoelasticity in directing lumen formation remains unknown. Here, viscoelastic alginate hydrogels with independently tunable stress relaxation (viscoelasticity), stiffness, and arginine–glycine–aspartate (RGD) ligand density are used to study hiPSC morphogenesis in 3D culture. A phase diagram that shows how these properties control hiPSC morphogenesis is reported. Higher RGD density and fast stress relaxation promote hiPSC viability, proliferation, apicobasal polarization, and lumen formation, while slow stress relaxation at low RGD densities triggers hiPSC apoptosis. Notably, hiPSCs maintain pluripotency in alginate hydrogels for much longer times than is reported in rBM matrices. Lumen formation is regulated by actomyosin contractility and is accompanied by translocation of Yes‐associated protein (YAP) from the nucleus to the cytoplasm. The results reveal matrix viscoelasticity as a potent factor regulating stem cell morphogenesis and provide new insights into how engineered biomaterials may be leveraged to build organoids.