The boards of directors at large European companies overlap with each other to a sizable extent both within and across national borders. This could have important economic, political and management consequences. In this work we study in detail the topological structure of the networks that arise from this phenomenon. Using a comprehensive information database, we reconstruct the implicit networks of shared directorates among the top 300 European firms in 2005 and 2010, and suggest a number of novel ways to explore the trans-nationality of such business elite networks. Powerful community detection heuristics indicate that geography still plays an important role: there exist clear communities and they have a distinct national character. Nonetheless, from 2005 to 2010 we observe a densification of the boards interlocks network and a larger transnational orientation in its communities. Together with central actors and assortativity analyses, we provide statistical evidence that, at the level of corporate governance, Europe is getting closer.