Valorization of wheat bran (WB) into new high-value products is of great interest within the framework of sustainability and circular economy. In the present study, we utilized a multi-step approach to extract nutraceutical compounds (phenolic acids) from WB and improved its antioxidant and anti-inflammatory properties through using sequential hydrothermal and enzymatic hydrolysis. Thirteen commercial glycosidases differing in their specific activity were screened and compared for hydrolytic efficiency to release monosaccharides, ferulic acid, and diferulic acid. Ultraflo XL was selected as the desired enzyme treatment on the basis of its higher WB solubilization, as well as its monosaccharide and phenolic acids yields. The relationships between better hydrolytic performance of Ultraflo XL and its particular activity profile were established. To determine the optimum conditions for Ultraflo XL treatment, we tested different factors (solvent pH, incubation temperature, and time) under 15 experiments. A multicomponent analysis (MCA), including central composite design, model fitness, regression coefficients, analysis of variance, 3D response curves, and desirability, was used for processing optimization. A beneficial effect of autoclave treatment on the release of phenolic compounds was also evidenced. The results of MCA showed involvement of linear, quadratic, and interactive effects of processing factors, although solvent pH was the main determinant factor, affecting enzymatic extraction of phenolics and bioactivity of hydrolysates. As compared to control WB, under optimized conditions (47 °C, pH = 4.4, and 20.8 h), WB hydrolysates showed 4.2, 1.5, 2, and 3 times higher content of ferulic acid (FA) and capacity to scavenge oxygen radicals, chelate transition metals, and inhibit monocyte chemoattractant protein-1 secretion in macrophages, respectively. These approaches could be applied for the sustainable utilization of WB, harnessing its nutraceutical potential.