The worldwide expansion of modern humans (Homo sapiens) from Africa started before the extinction of Neanderthals (Homo neanderthalensis). Both species coexisted and interbred, as revealed by the sequencing of Neanderthal genomes, leading to ~2% Neanderthal DNA in modern Eurasians, with slightly higher introgression in East Asians than in Europeans. These distinct levels of ancestry have been argued to result from selection processes. However, recent theoretical simulations have shown that range expansions could be another explanation. This hypothesis would lead to the generation of spatial gradients of introgression, increasing with the distance from the source of the expansion, i.e., Africa for modern humans. Here, we investigate the presence of Neanderthal introgression gradients after past human expansions by analysing an extended palaeogenomic dataset of Eurasian populations. Our results show that the Out-of-Africa expansion of modern humans into Eurasia resulted in spatial gradients of Neanderthal ancestry that persisted through time. Moreover, while keeping the same gradient orientation, the expansion of early Neolithic farmers into western Eurasia contributed decisively to reducing the average level of Neandertal genomic introgression in European compared to Asian populations. This is because Neolithic farmers carried less Neanderthal DNA than preceding Palaeolithic hunter-gatherers. This study shows that inferences about past population dynamics within our species can be made from the spatiotemporal variation in archaic introgression.