Saffron (Crocus sativusL.) is a traditional Mediterranean plant whose stigmas are used to obtain the most expensive spice in the world. Nevertheless, there is a lack of sustainability in its production, since, to produce 1 kg of saffron, about 350 kg of tepals are discarded. Therefore, this study aimed to develop wheat and spelt breads enriched with saffron floral by-products at a ratio of 0, 2.5, 5, and 10% (w/w), respectively, and to evaluate their nutritional, physicochemical, functional, and sensory properties, as well as the stability of antioxidant compounds during the in vitro digestion. The results revealed that the addition of saffron floral by-products, especially at 10%, increased the dietary fiber content by 25–30% of traditional wheat and spelt breads; improved their mineral content (270–290 mg/100 g for K, 90–95 mg/100 g for Ca, 40–50 mg/100 g for Mg, and 15–18 mg/100 g for Fe); changed their textural properties; and significantly enhanced the phenolic content and antioxidant ability (at 5 and 10%), which remained stable throughout the in vitro oral and gastrointestinal digestion processes. From a sensory point of view, the addition of saffron flowers modified the organoleptic properties of breads. Thus, these novel vegan enriched breads could exert beneficial effects on human health after their intake, making saffron floral by-products suitable and sustainable ingredients to develop new functional foods such as healthier alternative vegan bakery products.