International migration data in Europe are collected by individual countries with separate collection systems and designs. As a result, reported data are inconsistent in availability, definition, and quality. In this article, we propose a Bayesian model to overcome the limitations of the various data sources. The focus is on estimating recent international migration flows among 31 countries in the European Union and European Free Trade Association from 2002 to 2008, using data collated by Eurostat. We also incorporate covariate information and information provided by experts on the effects of undercount, measurement, and accuracy of data collection systems. The methodology is integrated and produces a synthetic database with measures of uncertainty for international migration flows and other model parameters. Supplementary materials for this article are available online.