The biogeographic origin of the species‐rich steppe grasslands in central Europe has long been debated. The alternative hypotheses are long‐term species persistence in situ versus immigration from the south‐east, either after the last glacial maximum (LGM) or after the Neolithic landscape deforestation. We ask whether macroclimate‐based models of habitat suitability support either of these hypotheses and search for macroclimatically suitable ‘source areas' from which species could colonise the areas occupied in Europe today. We modelled habitat suitability for 104 species of the central European steppes and projected these models to 10 periods between the LGM and the present using downscaled CCSM3 simulations. By simulating postglacial migration, we identified potential source areas for each species in the LGM and mid‐Holocene and examined whether their location differed among three ecological and five chorological species groups.The central European macroclimate during the cold phases of the Late Pleistocene was suitable for species now typical of Asian desert steppes, whereas the warmer Bølling–Allerød and Holocene macroclimates supported the occurrence of present‐day central European steppe flora. The models suggest that the LGM source areas of these species ranged from south‐eastern France through the Adriatic region and the Balkan Peninsula to the Black‐Sea region but extended to central Europe in the mid‐Holocene. Their locations differed considerably among ecological and chorological groups in both periods. Therefore, our models support the hypothesis that during the Pleistocene cold periods, the largest populations of these species occurred in southern and south‐eastern Europe and some of them may have later colonised central Europe. If some populations occurred in central Europe during the LGM, as suggested by recent genetic analyses, they were likely restricted to microrefugia embedded in the landscape matrix of species‐poor cold steppe. The precipitation‐rich mid‐Holocene climate had no direct negative impact on the central European steppe flora.