We propose a novel perspective on migration and cultural change by asking both theoretically and empirically - and from a global viewpoint - whether migration makes home and host countries culturally more similar. Our theoretical model derives distinctive testable predictions as to the sign and direction of cultural convergence for various compositional and cultural diffusion mechanisms. We use the World Value Survey for 1981-2014 to build time-varying measures of cultural similarity for a large number of country pairs and exploit within country-pair variation over time. Our results support migration-based cultural convergence, with cultural remittances as its main driver.