Drought stress is one of the major constraints for crop production in the Sahel region of Africa. Here, we explore the potential to use natural genetic variation to build on the inherent drought tolerance of an elite sorghum cultivar, Teshale, that has been bred for Ethiopian conditions including chronic drought. We evaluated a backcross nested-association mapping population using 12 diverse founder lines crossed with Teshale under three drought-prone environments in Ethiopia. All 12 populations averaged higher head exsertion and lower leaf senescence than the recurrent parent in the two most stressful environments, reflecting new drought resilience mechanisms from the donors. A total of 154 quantitative trait loci (QTLs) were detected for eight drought-responsive traits, and their validity was supported by the fact that 113 (73.4%) overlapped with QTLs previously detected for the same traits, concentrated in regions previously associated with 'stay-green' traits. Allele effects showed that some favourable alleles are already present in the Ethiopian cultivar; however, the exotic donors offer rich scope for increasing drought resilience. Using model-selected SNPs associated with the eight traits identified in this study and three in a companion study, phenotypic prediction accuracies for grain yield were equivalent to genome-wide SNPs and were significantly better than random SNPs, indicating that the selected traits are predictive of sorghum grain yield.