Epithelial cells migrate across wounds to repair injured tissue. Leader cells at the front of migrating sheets often drive this process. However, it is unclear how leaders emerge from an apparently homogeneous epithelial cell population. We characterized leaders emerging from epithelial monolayers in cell culture and found that they activated the stress sensor p53, which was sufficient to initiate leader cell behavior. p53 activated the cell cycle inhibitor p21^WAF1/CIP1, which in turn induced leader behavior through inhibition of cyclin-dependent kinase activity. p53 also induced crowding hypersensitivity in leader cells such that, upon epithelial closure, they were eliminated by cell competition. Thus, mechanically induced p53 directs emergence of a transient population of leader cells that drive migration and ensures their clearance upon epithelial repair.