The current dietary habits cause health problems due to foods’ composition, with bread as an important example. Our aim was to formulate an optimum dough blend with flours from wheat, amaranth and orange sweet potato to obtain a physically good and highly nutritional bread. Bread was prepared with blends of wheat, amaranth and orange sweet potato flours, optimizing the technological properties of the doughs by the response surface methodology and analyzing their physical and nutritional properties. Amaranth provides protein and fiber, and sweet potatoes provide β-carotenoids and high antioxidant activity. The prediction models were adjusted by mixing time (MT), peak dough resistance (PDR), setback (SB) and breakdown (BD). The interaction between wheat and amaranth significantly (p < 0.05) affected MT, PDR and SB, while the interaction between amaranth and sweet potato affected BD (p < 0.05); none of the components influenced PDR. The optimized blend (68.7% wheat, 22.7% amaranth and 8.6% sweet potato) produced a bread with the best crust and crumb appearance. This bread was comparable to that made with 100% wheat in specific volume and textural characteristics, but had better protein quality, higher content of fermentable fiber, pro-vitamin A, and bioactive compounds with good antioxidant capacity, and a lower glycemic index.