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While South Americans are underrepresented in human genomic diversity studies, Brazil has been a classical model for population genetics studies on admixture. We present the results of the EPIGEN Brazil Initiative, the most comprehensive up-to-date genomic analysis of any Latin-American population. A population-based genome-wide analysis of 6,487 individuals was performed in the context of worldwide genomic diversity to elucidate how ancestry, kinship, and inbreeding interact in three populations with different histories from the Northeast (African ancestry: 50%), Southeast, and South (both with European ancestry >70%) of Brazil. We showed that ancestry-positive assortative mating permeated Brazilian history. We traced European ancestry in the Southeast/South to a wider European/Middle Eastern region with respect to the Northeast, where ancestry seems restricted to Iberia. By developing an approximate Bayesian computation framework, we infer more recent European immigration to the Southeast/South than to the Northeast. Also, the observed low Native-American ancestry (6-8%) was mostly introduced in different regions of Brazil soon after the European Conquest. We broadened our understanding of the African diaspora, the major destination of which was Brazil, by revealing that Brazilians display two within-Africa ancestry components: one associated with non-Bantu/western Africans (more evident in the Northeast and African Americans) and one associated with Bantu/eastern Africans (more present in the Southeast/South). Furthermore, the whole-genome analysis of 30 individuals (42-fold deep coverage) shows that continental admixture rather than local post-Columbian history is the main and complex determinant of the individual amount of deleterious genotypes.