Grain amaranth is a pseudo-cereal and an ancient crop of Central and South America. Of the three species of grain amaranth, Amaranthus caudatus is mainly grown in the Andean region. Several models of domestication were proposed including a domestication from the wild relatives A. hybridus or A. quitensis. To investigate the domestication history of A. caudatus and its relationship to the two wild relatives, we used genotyping-by-sequencing (GBS) to genotype 119 amaranth accessions from the Andean region. We determined the genome sizes of the three species and compared phenotypic variation in two domestication-related traits, seed size and seed color. We show that the population genetic analysis based on 9,485 SNPs revealed very little genetic differentiation between the two wild species, suggesting they are the same species, but a strong differentiation between wild and domesticated amaranths. A. caudatus has a higher genetic diversity than its wild relatives and about 10% of accessions showed a strong admixture between the wild and cultivated species suggesting recent gene flow. Genome sizes and seed sizes were not significantly different between wild and domesticated amaranths, although a genetically distinct cluster of Bolivian accessions had significantly larger seeds.