The objective of this investigation was to evaluate the effects generated by amaranth flour (AF)—of different particle sizes (PS) added to white wheat flour from 0% to 20%—on the proximate composition, dough rheological behavior, and bread technological parameters. The reduction of particle size led to an increased hydration capacity of the wheat–amaranth composite flour, while bulk density decreased. Increasing the amount of AF and decreasing the PS led to a significant increase in protein, lipids, and ash contents, while the moisture and carbohydrates of the composite flour decreased. Increasing AF addition led to an increase in dough tenacity and a decrease in dough extensibility, while the PS had an irregular trend. The large particle size, at 15% and 20% levels of AF in wheat flour, increased significantly (p < 0.001) the dough tenacity and hardness, bread firmness, but decreased bread volume, porosity, and elasticity, while medium and small particles at 5–15% addition levels improved porosity and elasticity of the composite bread. Significant correlations (p < 0.05) were found between proximate composition, dough rheological characteristics, and bread quality for the wheat–amaranth composite flours. The results of this study are an important basis for the development of innovative wheat–amaranth bread recipes.