Grain amaranths (Amaranthus spp.) are ancient crops from the Americas that are consumed as pseudo-cereals and vegetables. Two grain amaranths, A. cruentus and A. hypochondriacus, originated in Central America, and A. caudatus in South America. Flowering time variation plays a central role in their uses as seed, vegetable and biomass crops. We characterized phenotypic variation for plant height, flowering time and seed setting among 253 genebank accessions including three grain and two wild ancestor species (A. hybridus and A. quitensis) in the temperate climatic and long-day conditions of Germany. Among grain amaranths, A. cruentus flowered early and 88% of the accessions set seed. A. hypochondriacus accessions were mildly or highly photoperiod-sensitive with a lower proportion of seed setting (31%). A. caudatus accessions were mildly photoperiod-sensitive and failed seed production. Photoperiod-insensitive accessions set seed regardless of their origin, and mildly photoperiod-sensitive accessions set seed if they originated from regions with higher temperatures. Overall, Central American accessions of both wild and domesticated amaranths showed large variation in flowering time and photoperiod sensitivity, whereas variation among South American wild and domesticated amaranths was limited to mild photoperiod sensitivity. This observation is consistent with a model of independent domestication in Central and South America, and suggests a potential Central American origin of A. hybridus followed by migration to and selection against high photoperiod sensitivity in South America. Our results provide useful information for the design of breeding programs for different uses, and provide insights into grain amaranth domestication by considering flowering time as an adaptive trait.