This research examines several modellers of immigration flows deployed within the European Union (EU), as well as their economic consequences upon the most targeted ten migrant receiving countries. The paper’s aim is to identify specific ways in which migrants can contribute to host countries’ sustainable development through positive spillover upon natives, labour market performance, and the overall economic activity. A set of methods and macro-econometric models, based on country fixed effects, spatial analysis, and structural equations modelling, was applied on a balanced panel formed by ten EU host economies. We analysed distinctly the labour and humanitarian (asylum seekers) migration flows, considered throughout two separate time periods, namely 2000–2015 and 2000–2019 (2019 being the deadline for Brexit negotiations). The results highlight that the immigration flows were mainly shaped by labour market outcomes, while the primary positive immigration impact was induced upon the gross domestic product (GDP) per capita and employment levels, both for natives and the foreign population.