The American Eel (Anguilla rostrata) has long been regarded as a panmictic fish and has been confirmed as such in the northern part of its range. In this paper, we tested for the first time whether panmixia extends to the tropical range of the species. To do so, we first assembled a reference genome (975 Mbp, 19 chromosomes) in order to support both this study and future research. To test for population structure, we estimated genotype likelihoods from low coverage whole genome sequencing of 460 American Eels, collected at 21 sampling sites (in seven geographic regions) ranging from Canada to Trinidad and Tobago. We estimated genetic distance between regions, performed ADMIXTURE-like clustering analysis and multivariate analysis, and found no evidence of population structure. In addition, two genomic regions with putative inversions were observed, both geographically widespread and present at similar frequencies in all regions. We discuss the implications of lack of genetic population structure for the species. Our results are key for the future genomic research in the American Eel and the implementation of conservation measures throughout its geographic range.