Drought is a major constraint on plant productivity globally. Sorghum [Sorghum bicolor (L.) Moench] landraces have evolved in drought-prone regions, but the genetics of their adaptation is poorly understood. Here we sought to identify novel drought-tolerance loci and test hypotheses on the role of known loci including those underlying stay-green (Stg) postflowering drought tolerance. We phenotyped 590 diverse sorghum accessions from West Africa in 10 environments, under field-based managed drought stress [preflowering water stress (WS1), postflowering water stress (WS2), and well-watered (WW)] and rainfed (RF) conditions over 4 yr. Days to 50% flowering (DFLo), aboveground dry biomass (DBM), plant height (PH), and plant grain yield components (including grain weight [GrW], panicle weight [PW] and grain number [GrN] per plant, and 1000-grain weight [TGrW]) were measured, and genome-wide association studies (GWAS) was conducted. Broad-sense heritability for biomass and plant grain yield was high (33–92%) across environments. There was a significant correlation between stress tolerance index (STI) for GrW per plant across WS1 and WS2. Genome-wide association studies revealed that SbZfl1 and SbCN12, orthologs of maize (Zea mays L.) flowering genes, likely underlie flowering time variation under these conditions. Genome-wide association studies further identified associations (n = 134; common between two GWAS models) for STI and drought effects on plant yield components including 16 putative pleiotropic associations. Thirty of the associations colocalized with Stg1, Stg2, Stg3, and Stg4 loci and had large effects. Seven lead associations, including some within Stg1, overlapped with positive selection outliers. Our findings reveal previously undescribed natural genetic variation for drought-tolerance-related traits and suggest a broad role of Stg loci in drought adaptation of sorghum.