The effect of fortification of wheat rolls with 1–5% Greek oregano on the profile of phytochemicals, their changes during processing and simulated digestion (with special emphasis on rosmarinic acid), and in vitro protein and starch digestibility was assessed. Additionally, the main functional properties, e.g. the basic technological quality (baking loss, total volume, specific volume, density, porosity), rosmarinic acid distribution, and consumer acceptance of the fortified products were investigated. Rosmarinic acid content (HPLC analysis), total phenolic content, and in vitro antioxidant activities (ABTS, DPPH, FRAP) were determined. These parameters were analyzed during the preparation, processing, and simulated digestion (at the gastric and intestinal phase) of rolls. Potential bioaccessibility was calculated based on the digestion results. The fortification significantly improved rosmarinic acid content, total phenolic content, and antioxidant activity of the rolls. The potential bioaccessibility of phytochemicals was relatively good, especially at the intestinal phase. Nonetheless, higher doses of the supplement negatively affected the nutrient digestibility and the functional properties of the rolls. Regarding nutraceutical potential, fortified rolls seem to be a good food vehicle for Greek oregano phytochemicals, however, simultaneous optimization of nutritional and functional parameters seems to be challenging due to the multiple and often unpredictable factors affecting the final quality of fortified products.