Last year, 3.8 percent of EU citizens of working age (20-64) were living in another member state than that of their citizenship, the agency said.

"This share has increased from 2.5 percent 10 years ago," it said. "The situation varies among member states, ranging from one percent for working-age citizens of Germany to 19.7 percent for citizens of Romania."

Data showed the next-largest shares were seen in Lithuania (15 percent), Croatia (14 percent), and Portugal (13.9 percent), while the EU member states with the smallest share of mobile nationals after Germany were the United Kingdom (1.1 percent), followed by Sweden and France (both 1.3 percent).

Eurostat said the free movement of workers is a fundamental principle of the EU.

"EU citizens are entitled to look for a job in another EU country, work there without a work permit, live there and enjoy equal treatment with nationals in access to employment, working conditions and all other social and tax advantages," it said.