Demographic models of Latin American populations often fail to fully capture their complex evolutionary history, which has been shaped by both recent admixture and deeper-in-time demographic events. To address this gap, we used high-coverage whole-genome data from Indigenous American ancestries in present-day Mexico and existing genomes from across Latin America to infer multiple demographic models that capture the impact of different timescales on genetic diversity. Our approach, which combines analyses of allele frequencies and ancestry tract length distributions, represents a significant improvement over current models in predicting patterns of genetic variation in admixed Latin American populations. We jointly modeled the contribution of European, African, East Asian, and Indigenous American ancestries into present-day Latin American populations. We infer that the ancestors of Indigenous Americans and East Asians diverged ∼30 thousand years ago, and we characterize genetic contributions of recent migrations from East and Southeast Asia to Peru and Mexico. Our inferred demographic histories are consistent across different genomic regions and annotations, suggesting that our inferences are robust to the potential effects of linked selection. In conjunction with published distributions of fitness effects for new nonsynonymous mutations in humans, we show in large-scale simulations that our models recover important features of both neutral and deleterious variation. By providing a more realistic framework for understanding the evolutionary history of Latin American populations, our models can help address the historical under-representation of admixed groups in genomics research and can be a valuable resource for future studies of populations with complex admixture and demographic histories., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 American Society of Human Genetics. Published by Elsevier Inc. All rights reserved.)