Using a specially constructed international dataset of adult heights, we assess the extent, drivers and consequences of migrant selectivity, measured as relative height. This offers a measure of health selectivity that precedes emigration and is stable over time. Applying this measure to representative data from the German Socio-Economic Panel, we (i) evaluate whether it correlates with characteristics theoretically associated with migrant health selectivity, (ii) test the assumption that selectivity accounts for the commonly observed immigrant health advantage, and (iii) assess whether degree of selectivity sheds light on the paradox that immigrants' health deteriorates over time since arrival. We find that while, on average, immigrants are positively selected on health and have better health on average than non-migrant Germans, greater selectivity is not associated with better health. However, more positively selected immigrants experience less deterioration in their health, whether evaluated cross-sectionally across arrival cohorts or longitudinally within individuals, helping to explain the immigrant health paradox. Overall, our results i) confirm that migrants are selected on health, ii) support theoretical expectations relating to migrant selection that higher barriers to migration increase selectivity, and iii) demonstrate that while most immigrants are healthier upon arrival, only more selected immigrants enjoy better health throughout adulthood.