This paper investigates the effects of labour migration and openness to trade on regional skill endowments across the European Union at a time of increased economic integration. Using regional data from Eurostat's Regio database and the open web source Openflight for the period 1998-2010 we test whether the spatial concentration of skills has increased or decreased over time. We account for neighboring effects associated with both geographic proximity and links through civilian flights using a random spatial effect model. We find that migration contributes to convergence in regional skill endowments across member states, particularly at the Southern and Eastern periphery of the European Union. We also find that inter-regional connectivity through civilian flights has much stronger effects on the evolution of a region's skill endowment than geographic contiguity.