The extent to which international high-skilled mobility channels are forming is a question of great importance in an increasingly global knowledge-based economy. One factor facilitating the growth of high-skilled labour markets is the standardization of certifiable degrees meriting international recognition. Within this context, we analysed an extensive high-skilled mobility database comprising roughly 382 000 individuals from five broad profession groups (Medical, Education, Technical, Science & Engineering and Business & Legal) over the period 1997–2014, using the 13-country expansion of the European Union (EU) to provide insight into labour market integration. We compare the periods before and after the 2004 enlargement, showing the emergence of a new east–west migration channel between the 13 mostly eastern EU entrants (E) and the rest of the western European countries (W). Indeed, we observe a net directional loss of human capital from E → W, representing 29% of the total mobility after 2004. Nevertheless, the counter-migration from W → E is 7% of the total mobility over the same period, signalling the emergence of brain circulation within the EU. Our analysis of the country–country mobility networks and the country–profession bipartite networks provides timely quantitative evidence for the convergent integration of the EU, and highlights the central role of the UK and Germany as high-skilled labour hubs. We conclude with two data-driven models to explore the structural dynamics of the mobility networks. First, we develop a reconfiguration model to explore the potential ramifications of Brexit and the degree to which redirection of high-skilled labourers away from the UK may impact the integration of the rest of the European mobility network. Second, we use a panel regression model to explain empirical high-skilled mobility rates in terms of various economic ‘push–pull’ factors, the results of which show that government expenditure on education, per capita wealth, geographical proximity and labour force size are significant attractive features of destination countries.