The purpose of our study was to evaluate the potential of solid-state yeast fermentation (SSYF) in improving the phenolic acid content and composition, and the antioxidant activity of commercial wheat bran (WB) and oat bran (OB). The ultrasound-assisted methanolic extracts were compared for their total phenolic content (TPC), phenolics composition, and in vitro antioxidant activity in order to study the effect of fermentation time on the chemical profile and activity of bioactive compounds. The comparative analysis revealed significant differences (p < 0.05) between days of fermentation (0 through 6). The highest TPCs were obtained on day 3 for WB (0.84 ± 0.05 mg of gallic acid equivalents [GAE]/g dry weight [DW]), and on day 4 for OB (0.45 ± 0.02 mg GAE/g DW). The highest relative percentage increase in the phenolics concentration of WB was also registered on day 3 (ferulic acid +56.6%, vanillic acid +259.3%, dihydroxybenzoic acids +161.2%, apigenin-glucoside +15.3%); for OB, this was observed on day 4 (avenanthramide 2f +48.5%, ferulic acid +21.2%). Enhanced antioxidant activities were significantly correlated with the highest TPCs. Our results suggest that SSYF may be a useful procedure for enrichment of antioxidants in cereal bran, considering the design of different functional foods and nutraceuticals.