Bread is a staple food and can be a potential product to be enriched with various deficient nutrients. The objective of the study was to characterize the nutritional properties of toasted bread enriched with 10% and 20% of kale and wholemeal bread with 20% and 40% of spinach. The supplementation increased the phenolic content up to 2–3 times in the bread with the addition of 20% spinach and 40% kale. The highest antioxidant properties were noticed in extracts of bread with 20% kale. The in vitro digestion released the hydrophilic and lipophilic antioxidative compounds, leading to higher bioaccessibility of the breads enriched with these selected green vegetables. Even more than a 2-fold increase in folate content was observed in breads with the greatest addition of kale (20%) and spinach (40%), from 18.1 to 45.3 µg/100 g and from 37.2 to 83.2 µg/100 g, respectively, compared to the non-enriched breads. Breads with spinach showed significantly (P < 0.05) higher contents of all of the tested minerals, Cu, Mn, Fe, Zn, Mg, Ca, Na, K, and P, whereas kale enriched breads showed most of them. The results suggest that the addition of fresh green vegetables can enhance the daily supply of micronutrients and significantly increase the bioavailability of bioactive compounds with high antioxidant status.