Leaf (brown) rust (LR) and stripe (yellow) rust (YR), caused by Puccinia triticina and P. striiformis f. sp. tritici, respectively, significantly reduce wheat production worldwide. Disease-resistant wheat varieties offer farmers one of the most effective ways to manage these diseases. The common wheat (Triticum aestivum L.) Arableu#1, developed by the International Maize and Wheat Improvement Center and released as Deka in Ethiopia, shows susceptibility to both LR and YR at the seedling stage but a high level of adult plant resistance (APR) to the diseases in the field. We used 142 F5 recombinant inbred lines (RILs) derived from Apav#1 × Arableu#1 to identify quantitative trait loci (QTLs) for APR to LR and YR. A total of 4,298 genotyping-by-sequencing markers were used to construct a genetic linkage map. The study identified four LR resistance QTLs and six YR resistance QTLs in the population. Among these, QLr.cim-1BL.1/QYr.cim-1BL.1 was located in the same location as Lr46/Yr29, a known pleiotropic resistance gene. QLr.cim-1BL.2 and QYr.cim-1BL.2 were also located on wheat chromosome 1BL at 37 cM from Lr46/Yr29 and may represent a new segment for pleiotropic resistance to both rusts. QLr.cim-7BL is likely Lr68 given its association with the tightly linked molecular marker cs7BLNLRR. In addition, QLr.cim-3DS, QYr.cim-2AL, QYr.cim-4BL, QYr.cim-5AL, and QYr.cim-7DS are probably new resistance loci based on comparisons with published QTLs for resistance to LR and YR. Our results showed the diversity of minor resistance QTLs in Arableu#1 and their role in conferring near-immune levels of APR to both LR and YR, when combined with the pleiotropic APR gene Lr46/Yr29.