Fruit pomace is a highly valuable byproduct from a nutritional standpoint. The aim of this study was to determine the physicochemical and sensory properties of wheat bread enriched with freeze-dried and powdered chokeberry pomace in amounts of 1, 2, 3, 4, 5, and 6% relative to the flour weight. The influence of pomace addition on the physical properties of the wheat dough was analyzed, and the physicochemical properties and consumer acceptance of the chokeberry-pomace-enriched bread were determined. Based on the obtained research results, it was shown that the addition of pomace increased the water absorption of the flour but caused a decrease in stability and weakening of the dough, resulting in increased softening. Consequently, the volume of the bread decreased, and the crumb hardness increased. Furthermore, the addition of pomace significantly reduced the brightness and yellowness of the bread crumbs, while making them more red. Importantly, compared to the control bread, the pomace-enriched bread was characterized by higher contents of minerals, dietary fiber, phenolic compounds, and higher antioxidant activity. Sensory evaluation showed that the addition of freeze-dried chokeberry pomace to wheat bread should not exceed 3% in relation to the weight of the flour used. Additionally, a 3% addition of chokeberry pomace increased the dietary fiber content by 80.9%, ash content by 2.6%, fat content by 26.5%, and total phenolics content by 272%. It decreased the protein content by 1.2%, and reduced the carbohydrate content by 4% compared to the control sample.