Identifying drought-tolerant crops/genotypes may provide a sustainable solution to improve productivity on rain-fed sodic soils. However, the identification of genotypes tolerant to sodicity has been impeded by a lack of suitable, high-throughput techniques. Here, we propose an unmanned aerial vehicle remote sensing coupled with field experimental approach to evaluate drought tolerance and/or water use of contrasting wheat genotypes by quantifying Genotype × Environment interactions on rain-fed moderately sodic and highly sodic soil sites in Australia. Significant differences (p < 0.05) between the sites and some between genotypes were observed based on remote sensing-based vegetative drought indices, while in-season agro-climatic and soil moisture conditions were similar (p > 0.10) between the sites. This suggests that genotypes at both sites would have grown with similar access to moisture if differences in soil constraints had not been present. Further, as a useful indicator of drought, a crop health index was computed by integrating drought vegetative and temperature response variables that significantly correlated with wheat yield (coefficient of determination R2 = 0.67; root mean square error RMSE = 28.4 g m−2 and R2 = 0.41; RMSE = 33.6 g m−2 for the moderately sodic and highly sodic site, respectively). Further, a drought stress tolerance index was developed using estimates of yield anomaly between the sites to differentiate genotypes tolerant to drought on sodic soils. Genotypic ranking to drought tolerance was further compared and validated with actual field measured crop water use efficiency data. Wheat genotypes Bremer and Gladius were identified as the most and least tolerant to drought on sodic soils. The research improves our understanding of genotypic response in drought stress and can assist farmers in the selection of drought-tolerant wheat genotypes in sodic soil environments.