The issues of the forced migration on the one side and the integration of refugees in the EU society and labour markets on the other side are high on the policy agenda. Apart from humanitarian aspects, a sustainable integration of accepted asylum seekers is important also for social, economic, budgetary and other reasons. Although the potential socioeconomic consequences of accepted asylum seekers often are being discussed, little scientific evidence has supported the policy debate in the context of the current refugee crisis in the EU so far. This study attempts to shed light on the long‐run social, economic and budgetary effects of the rapidly increasing forced immigration into the EU by performing a holistic analysis of alternative refugee integration scenarios. Our simulation results suggest that, although the refugee integration, for example, by the providing language and professional training, is costly for the public budget, in the medium to long‐run, the social, economic and fiscal benefits may significantly outweigh the short‐run refugee integration costs. Depending on the integration policy scenario and policy financing method, the annual long‐run GDP effect would be 0.2%–1.6% above the baseline growth.