Throughout human evolutionary history, large-scale migrations have led to intermixing (i.e., admixture) between previously separated human groups. While classical and recent work have shown that studying admixture can yield novel historical insights, the extent to which this process contributed to adaptation remains underexplored. Here, we introduce a novel statistical model, specific to admixed populations, that identifies loci under selection while determining whether the selection likely occurred post-admixture or prior to admixture in one of the ancestral source populations. Through extensive simulations we show that this method is able to detect selection, even in recently formed admixed populations, and to accurately differentiate between selection occurring in the ancestral or admixed population. We apply this method to genome-wide SNP data of ~4,000 individuals in five admixed Latin American cohorts from Brazil, Chile, Colombia, Mexico and Peru. Our approach replicates previous reports of selection in the HLA region that are consistent with selection post-admixture. We also report novel signals of selection in genomic regions spanning 47 genes, reinforcing many of these signals with an alternative, commonly-used local-ancestry-inference approach. These signals include several genes involved in immunity, which may reflect responses to endemic pathogens of the Americas and to the challenge of infectious disease brought by European contact. In addition, some of the strongest signals inferred to be under selection in the Native American ancestral groups of modern Latin Americans overlap with genes implicated in energy metabolism phenotypes, plausibly reflecting adaptations to novel dietary sources available in the Americas.