Migration has become a significant source of population change at the global level, with broad societal implications. Although understanding the drivers of migration is critical to enacting effective policies, theoretical advances in the study of migration processes have been limited by the lack of data on flows of migrants, or by the fragmented nature of these flows. In this paper, we build on existing Bayesian modeling strategies to develop a statistical framework for integrating different types of data on migration flows. We offer estimates, as well as associated measures of uncertainty, for immigration, emigration, and net migration flows among 31 European countries, by combining administrative and household survey data from 2002 to 2015. Substantively, we document the historical impact of the EU enlargement and the free movement of workers in Europe on migration flows.