Response to photoperiod is of major importance in crop production. It defines the adaptation of plants to local environments. Quinoa is a short-day plant which had been domesticated in the Andeans regions. We wanted to understand the adaptation to long-day conditions by studying orthologues of two major flowering time regulators of Arabidopsis, FLOWERING LOCUS T (FT) and CONSTANS (CO) in quinoa accessions with contrasting photoperiod response. By searching the quinoa reference genome sequence, we identified 24 FT and six CO homologs. CqFT genes displayed remarkably different expression patterns between long- and short-day conditions, whereas the influence of the photoperiod on CqCOL expressions was moderate. Cultivation of 276 quinoa accessions under short- and long-day conditions revealed great differences in photoperiod sensitivity. After sequencing their genomes, we identified large sequence variations in 12 flowering time genes. We found non-random distribution of haplotypes across accessions from different geographical origins, highlighting the role of CqFT and CqCOL genes in the adaptation to different day-length conditions. We identified five haplotypes causing early flowering under long days. This study provides assets for quinoa breeding because superior haplotypes can be assembled in a predictive breeding approach to produce well-adapted early flowering lines under long-day photoperiods.