Atomistic simulations of radiation damage uncover how grain boundaries (GBs) migrate and coalesce under irradiation in bicrystalline Cu. Planar GB migration biased by defect cluster-mediated attraction first leads to slow and steady motion. Subsequently, adjoining GBs coalesce into curved surfaces, where curvature-driven migration with a velocity three orders of magnitude higher than that of a planar boundary dominates motion, triggering rapid grain growth. This study reveals the atomistic mechanisms of radiation-induced grain growth, and has practical implications towards engineering radiation-tolerant nanostructures.