Historical records and genetic analyses indicate that Latin Americans trace their ancestry mainly to the intermixing (admixture) of Native Americans, Europeans and Sub-Saharan Africans. Using novel haplotype-based methods, here we infer sub-continental ancestry in over 6,500 Latin Americans and evaluate the impact of regional ancestry variation on physical appearance. We find that Native American ancestry components in Latin Americans correspond geographically to the present-day genetic structure of Native groups, and that sources of non-Native ancestry, and admixture timings, match documented migratory flows. We also detect South/East Mediterranean ancestry across Latin America, probably stemming mostly from the clandestine colonial migration of Christian converts of non-European origin (Conversos). Furthermore, we find that ancestry related to highland (Central Andean) versus lowland (Mapuche) Natives is associated with variation in facial features, particularly nose morphology, and detect significant differences in allele frequencies between these groups at loci previously associated with nose morphology in this sample.