Potato (Solanum tuberosum L.) is an important tuber crop that is highly affected by poor soil fertility and nutrient disparities. Nutrient depletion due to intensive monocropping and poor soil management practices is a serious problem in Ethiopia, including in northwestern areas. Therefore, an experiment was conducted in the East Gojjam zone of northwestern Ethiopia to evaluate the influence of phosphorus and potassium fertilizer rates on potato tuber production. Three phosphorus levels (0, 34.5, and 69 kg/ha−1) and four potassium levels (0, 100, 200, and 300 kg/ha−1) were set out in a factorial arrangement and replicated three times using a randomized complete block design. Data on growth and quality parameters, as well as plant tissue analysis results, were collected. According to the results, the main effects of phosphorus and potassium fertilizer rates statistically affected growth components. The combined effects of phosphorus and potassium fertilizers had a significant influence on quality components (tuber size distribution). Similarly, the interaction effects of phosphorus and potassium fertilizer rates gave the highest response in all nutrient use efficiency parameters. The combined application of 34.5 kg P2O5 and 200 kg K2O fertilizers resulted in the highest medium (28.32 ton/ha−1) and large-sized (20.0 ton/ha−1) tuber yields. The interaction effect of 34.5 kg P2O5 with 100 kg K2O ha−1 yielded the highest agronomic and recovery efficiency values. Hence, a combination of 34.5 kg P2O5 ha−1 and 200 kg K2O ha−1 fertilizer rates can be recommended for the optimal production of potato in the northwestern area.