The accumulation of genome-wide molecular data has emphasized the important role of hybridization in the evolution of many organisms, which may carry introgressed genomic segments resulting from past admixture events with other taxa. Despite a number of examples of hybridization occurring during biological invasions, the resulting spatial patterns of genomic introgression remain poorly understood. Preliminary simulation studies have suggested a heterogeneous spatial level of introgression for invasive taxa after range expansion. We investigated in detail the robustness of this pattern and its persistence over time for both invasive and local organisms. Using spatially explicit simulations, we explored the spatial distribution of introgression across the area of colonization of an invasive taxon hybridizing with a local taxon. The general pattern for neutral loci supported by our results is an increasing introgression of local genes into the invasive taxon with the increase in the distance from the source of the invasion and a decreasing introgression of invasive genes into the local taxon. However, we also show there is some variation in this general trend depending on the scenario investigated. Spatial heterogeneity of introgression within a given taxon is thus an expected neutral pattern in structured populations after a biological invasion with a low to moderate amount of hybridization. We further show that this pattern is consistent with published empirical observations. Using additional simulations, we argue that the spatial pattern of Neanderthal introgression in modern humans, which has been documented to be higher in Asia than in Europe, can be explained by a model of hybridization with Neanderthals in Eurasia during the range expansion of modern humans from Africa. Our results support the view that weak hybridization during range expansion may explain spatially heterogeneous introgression patterns without the need to invoke selection.