Extruded snacks are commonly made with cereals with good expansion properties but low nutritional value. This study aimed to develop a nutrient-rich optimized extruded snack by incorporating orange-fleshed sweet potato, finger millet, and soybean flour. The extrusion processing conditions were optimized using a response surface method with a range of barrel temperature (90–130°C) and (20–26%) feed moisture content. Thirteen treatment combinations were generated for this experiment using response surface methods and face-centered central composite design. Standard methods were used to evaluate the effect of barrel temperature and feed moisture content on extruded snacks' nutritional, anti-nutritional, physical, functional, and sensory acceptability. The data were analyzed using Design Expert software version 13. Multiple regression analysis showed significant effects of the independent variables on moisture, protein, fat, beta-carotene, bulk density, hardness, expansion ratio, WAI, WSI, and overall acceptability of the extrudates. The optimum response of 14.06% protein, 3.26% ash, 69.12% carbohydrate, 6.477mg/100g beta-carotene, 0.36g/ml BD, 2.72mm/mm ER, 87.28N hardness, 4.34g/g WAI, 22.34% WSI, and overall acceptability of 3.30 was achieved at a barrel temperature of 114.5°C and feed moisture content of 20%. The extrusion processing conditions significantly impacted the resulting extrudates' nutritional value and other properties. These findings suggest that optimizing the extrusion processing conditions can lead to developing extruded snacks with desirable nutritional, physical, functional, and sensory properties.