During development, cells undergo symmetry breaking into differentiated subpopulations that self-organize into complex structures. However, few tools exist to recapitulate these behaviors in a controllable and coupled manner. Here, we engineer a stochastic recombinase genetic switch tunable by small molecules to induce programmable symmetry breaking, commitment to downstream cell fates, and morphological self-organization. Inducers determine commitment probabilities, generating tunable subpopulations as a function of inducer dosage. We use this switch to control the cell-cell adhesion properties of cells committed to each fate. We generate a wide variety of 3D morphologies from a monoclonal population and develop a computational model showing high concordance with experimental results, yielding new quantitative insights into the relationship between cell-cell adhesion strengths and downstream morphologies. We expect that programmable symmetry breaking, generating precise and tunable subpopulation ratios and coupled to structure formation, will serve as an integral component of the toolbox for complex tissue and organoid engineering.