South America has a complex demographic history shaped by multiple migration and admixture events in pre- and post-colonial times. Settled over 14,000 years ago by Native Americans, South America has experienced migrations of European and African individuals, similar to other regions in the Americas. However, the timing and magnitude of these events resulted in markedly different patterns of admixture throughout Latin America. We use genome-wide SNP data for 437 admixed individuals from 5 countries (Colombia, Ecuador, Peru, Chile, and Argentina) to explore the population structure and demographic history of South American Latinos. We combined these data with population reference panels from Africa, Asia, Europe and the Americas to perform global ancestry analysis and infer the subcontinental origin of the European and Native American ancestry components of the admixed individuals. By applying ancestry-specific PCA analyses we find that most of the European ancestry in South American Latinos is from the Iberian Peninsula; however, many individuals trace their ancestry back to Italy, especially within Argentina. We find a strong gradient in the Native American ancestry component of South American Latinos associated with country of origin and the geography of local indigenous populations. For example, Native American genomic segments in Peruvians show greater affinities with Andean indigenous peoples like Quechua and Aymara, whereas Native American haplotypes from Colombians tend to cluster with Amazonian and coastal tribes from northern South America. Using ancestry tract length analysis we modeled post-colonial South American migration history as the youngest in Latin America during European colonization (9-14 generations ago), with an additional strong pulse of European migration occurring between 3 and 9 generations ago. These genetic footprints can impact our understanding of population-level differences in biomedical traits and, thus, inform future medical genetic studies in the region.