Political and environmental factors-e.g., regional conflicts and global warming-increase large-scale migrations, posing extraordinary societal challenges to policymakers of destination countries. A common concern is that such a massive arrival of people-often from a country with a disrupted healthcare system-can increase the risk of vaccine-preventable disease outbreaks like measles. We analyze human flows of 3.5 million (M) Syrian refugees in Turkey inferred from massive mobile-phone data to verify this concern. We use multilayer modeling of interdependent social and epidemic dynamics to demonstrate that the risk of disease reemergence in Turkey, the main host country, can be dramatically reduced by 75 to 90% when the mixing of Turkish and Syrian populations is high. Our results suggest that maximizing the dispersal of refugees in the recipient population contributes to impede the spread of sustained measles epidemics, rather than favoring it. Targeted vaccination campaigns and policies enhancing social integration of refugees are the most effective strategies to reduce epidemic risks for all citizens.