Wnt signal transduction is mediated by a protein assembly called the Destruction Complex (DC) made from scaffold proteins and kinases that are essential for transducing extracellular Wnt ligand concentrations to changes in nuclear β-catenin, the pathway’s transcriptional effector. Recently, DC scaffold proteins have been shown to undergo liquid-liquid phase separation in vivo and in vitro providing evidence for a mesoscale organization of the DC. However, the mesoscale organization of DC at endogenous expression levels and how that organization could play a role in β-catenin processing is unknown. Here we find that the native mesoscale structure is a dynamic biomolecular condensate nucleated by the centrosome. Through a combination of advanced microscopy, CRISPR-engineered custom fluorescent tags, finite element simulations, and optogenetic tools, that allow for independent manipulation of the biophysical parameters that drive condensate formation, we find that a function of DC nucleation by the centrosome is to drive efficient processing of β-catenin by co-localizing DC components to a single reaction hub. We demonstrate that simply increasing the concentration of a single DC kinase onto the centrosome controls β-catenin processing. This simple change in localization completely alters the fate of the Wnt-driven human embryonic stem cell differentiation to mesoderm. Our findings demonstrate the role of nucleators in dynamically controlling the activities of biomolecular condensates and suggest a tight integration between cell cycle progression and Wnt signal transduction.