Determining the identity and distribution of molecular changes leading to the evolution of modern crop species provides major insights into the timing and nature of historical forces involved in rapid phenotypic evolution. In this study, we employed an integrated candidate gene strategy to identify loci involved in the evolution of flowering time during early domestication and modern improvement of the sunflower (Helianthus annuus). Sunflower homologs of many genes with known functions in flowering time were isolated and cataloged. Then, colocalization with previously mapped quantitative trait loci (QTLs), expression, or protein sequence differences between wild and domesticated sunflower, and molecular evolutionary signatures of selective sweeps were applied as step-wise criteria for narrowing down an original pool of 30 candidates. This process led to the discovery that five paralogs in the FLOWERING LOCUS T/TERMINAL FLOWER 1 gene family experienced selective sweeps during the evolution of cultivated sunflower and may be the causal loci underlying flowering time QTLs. Our findings suggest that gene duplication fosters evolutionary innovation and that natural variation in both coding and regulatory sequences of these paralogs responded to a complex history of artificial selection on flowering time during the evolution of cultivated sunflower.