The main objective of this study is to evaluate biogeographic hypotheses of diversification and connection between isolated savannas north (Amazonian savannas) and south (Cerrado core) of the Amazon River. To achieve our goal, we employed genomic markers (genotyping-by-sequencing) to evaluate the genetic structure, population phylogenetic relationships, and historical range shifts of four Neotropical passerines with peri-Atlantic distributions: the Narrow-billed Woodcreeper (Lepidocolaptes angustirostris), the Plain-crested Elaenia (Elaenia cristata), the Grassland Sparrow (Ammodramus humeralis), and the White-banded Tanager (Neothraupis fasciata). The population genetic analyses indicated that landscape (e.g., geographic distance, landscape resistance, and percentage of tree cover) and climate metrics explained divergence among populations in most species, but without indicating a differential role between current and historical factors. Our results did not fully support the hypothesis that isolated populations at Amazonian savannas have been recently derived from the Cerrado core domain. Intraspecific phylogenies and gene flow analyses supported multiple routes of connection between the Cerrado and Amazonian savannas, rejecting the hypothesis that the Atlantic corridor explains the peri-Atlantic distribution. Our results reveal that the biogeographic history of the region is complex and cannot be explained by simple vicariant models.