The progression of many solid tumors is accompanied by temporal and spatial changes in the stiffness of the extracellular matrix (ECM). Cancer cells adapt to soft and stiff ECM through mechanisms that are not fully understood. It is well known that there is significant genetic heterogeneity from cell to cell in tumors, but how ECM stiffness as a parameter might interact with that genetic variation is not known. Here, we employed experimental evolution to study the response of genetically variable and clonal populations of tumor cells to variable ECM stiffness. Proliferation rates of genetically variable populations cultured on soft ECM increased over a period of several weeks, whereas clonal populations did not evolve. Tracking of DNA barcoded cell lineages revealed that soft ECM consistently selected for the same few variants. These data provide evidence that ECM stiffness exerts natural selection on genetically variable tumor populations. Soft-selected cells were highly migratory, with enriched oncogenic signatures and unusual behaviors such as spreading and traction force generation on ECMs with stiffness as low as 1 kPa. Rho-regulated cell spreading was found to be the directly selected trait, with yes-associated protein 1 translocation to the nucleus mediating fitness on soft ECM. Overall, these data show that genetic variation can drive cancer cell adaptation to ECM stiffness.