European Union economies are pressed by (i) a demographic change that induces population ageing and a decline of the workforce, and (ii) a split labour market that is characterized by high levels of unemployment for low-skilled people and a simultaneous shortage of skilled workers. This lack of flexible high-skilled workers and the ageing process has created the image of an immobile labour force and the eurosklerosis phenomenon. In such a situation, an economically motivated immigration policy at the European level can generate welfare improvements. A selective policy that discourages unskilled migrants and attracts skilled foreign workers will vitalize the labour market, foster growth and increase demand for unskilled native workers. The paper summarizes the available economic insights, and suggests (i) the need to harmonize the single-country migration policies across Europe and (ii) that the European Union needs to become an active player on the international labour markets.