Both human embryonic stem cells and induced pluripotent stem cells can self-renew indefinitely in culture; however, present methods to clonally grow them are inefficient and poorly defined for genetic manipulation and therapeutic purposes. Here we develop the first chemically defined, xeno-free, feeder-free synthetic substrates to support robust self-renewal of fully dissociated human embryonic stem and induced pluripotent stem cells. Material properties including wettability, surface topography, surface chemistry and indentation elastic modulus of all polymeric substrates were quantified using high-throughput methods to develop structure–function relationships between material properties and biological performance. These analyses show that optimal human embryonic stem cell substrates are generated from monomers with high acrylate content, have a moderate wettability and employ integrin α_vβ₃ and α_vβ₅ engagement with adsorbed vitronectin to promote colony formation. The structure–function methodology employed herein provides a general framework for the combinatorial development of synthetic substrates for stem cell culture.