Genetic variation in contemporary South Asian populations follows a northwest to southeast decreasing cline of shared West Eurasian ancestry. A growing body of ancient DNA evidence is being used to build increasingly more realistic models of demographic changes in the last few thousand years. Through high-quality modern genomes, these models can be tested for gene and genome level deviations. Using local ancestry deconvolution and masking, we reconstructed population-specific surrogates of the two main ancestral components for more than 500 samples from 25 South Asian populations and showed our approach to be robust via coalescent simulations. Our f3 and f4 statistics-based estimates reveal that the reconstructed haplotypes are good proxies for the source populations that admixed in the area and point to complex interpopulation relationships within the West Eurasian component, compatible with multiple waves of arrival, as opposed to a simpler one wave scenario. Our approach also provides reliable local haplotypes for future downstream analyses. As one such example, the local ancestry deconvolution in South Asians reveals opposite selective pressures on two pigmentation genes (SLC45A2 and SLC24A5) that are common or fixed in West Eurasians, suggesting post-admixture purifying and positive selection signals, respectively.