Despite extensive work on the dynamics and outcomes of large-scale migrations, timely and accurate estimates of population movements do not exist. While censuses, surveys, and observational data have been used to measure migration, estimates based on these data sources are constrained in their inability to detect unfolding migrations, and lack temporal and demographic detail. In this study, we present a novel approach for generating estimates of migration that can measure movements of particular demographic groups across country lines. Specifically, we model migration as a function of long-term moves across countries using aggregated Facebook data. We demonstrate that this methodological approach can be used to produce accurate measures of past and ongoing migrations - both short-term patterns and long-term changes in residence. Several case studies confirm the validity of our approach, and highlight the tremendous potential of information obtained from online platforms to enable novel research on human migration events.