Summary Soil salinity and drought limit sweet potato yield. Scavenging of reactive oxygen species (ROS) by peroxidases (PRXs) is essential during plant stress responses, but how PRX expression is regulated under abiotic stress is not well understood. Here, we report that the B‐box (BBX) family transcription factor IbBBX24 activates the expression of the class III peroxidase gene IbPRX17 by binding to its promoter. Overexpression of IbBBX24 and IbPRX17 significantly improved the tolerance of sweet potato to salt and drought stresses, whereas reducing IbBBX24 expression increased their susceptibility. Under abiotic stress, IbBBX24‐ and IbPRX17‐overexpression lines showed higher peroxidase activity and lower H2O2 accumulation compared with the wild‐type. RNA sequencing analysis revealed that IbBBX24 modulates the expression of genes encoding ROS scavenging enzymes, including PRXs. Moreover, interaction between IbBBX24 and the APETALA2 (AP2) protein IbTOE3 enhances the ability of IbBBX24 to activate IbPRX17 transcription. Overexpression of IbTOE3 improved the tolerance of tobacco plants to salt and drought stresses by scavenging ROS. Together, our findings elucidate the mechanism underlying the IbBBX24–IbTOE3–IbPRX17 module in response to abiotic stress in sweet potato and identify candidate genes for developing elite crop varieties with enhanced abiotic stress tolerance.