Wnt signal transduction is controlled by the destruction complex (DC), a condensate comprising scaffold proteins and kinases that regulate β-catenin stability. Overexpressed DC scaffolds undergo liquid-liquid phase separation (LLPS), but DC mesoscale organization at endogenous expression levels and its role in β-catenin processing were previously unknown. Here, we find that DC LLPS is nucleated by the centrosome. Through a combination of CRISPR-engineered custom fluorescent tags, finite element simulations, and optogenetic tools that allow for manipulation of DC concentration and multivalency, we find that centrosomal nucleation drives processing of β-catenin by colocalizing DC components to a single reaction crucible. Enriching GSK3β partitioning on the centrosome controls β-catenin processing and prevents Wnt-driven embryonic stem cell differentiation to mesoderm. Our findings demonstrate the role of nucleators in controlling biomolecular condensates and suggest tight integration between Wnt signal transduction and the cell cycle.