Iron and zinc deficiencies in humans can cause serious health problems. Increasing the iron (IC) and zinc (ZC) concentrations in common bean (Phaseolus vulgaris L.) grains using genetic breeding can be an effective strategy to prevent these problems. Thus, the aims of this study were i) to investigate the importance of genetic, environmental, and genotype-by-environment interaction effects on IC and ZC in common bean grains; ii) to select cultivars that have high mean values and phenotypic stability for IC and ZC, as well as high protein concentration (PC), high yield, and standard commercial grain quality; and iii) to investigate whether there is a genetic relationship between these traits. A total of 34 cultivars were evaluated in 19 different environments. Genetic variability was observed among the genotypes for all traits. For IC and ZC, the environmental effect represented most of the total variation (63% and 65%, respectively), and the effect of the G × E interaction was 18% for IC and 15% for ZC. The genetic correlations between IC, ZC, and PC were positive, indicating that the selection of one of these traits resulted in gains for the other. The genetic correlations between IC or ZC with yield or 100-grain weight were low or intermediate, but negative, indicating that it is important to evaluate these traits at all stages of breeding programs that focus on developing cultivars with high IC and ZC. The cultivar BRS Sublime, with the carioca grain type, combined high IC, ZC, and PC, high yield, and grains of commercial size.