Grape pomace (GP) is considered a natural source of bioactive compounds. To improve the extractability of bioactive compounds, in this work, GP was biologically treated for 15 days with the white-rot fungus Trametes versicolor in laboratory jars and a tray bioreactor under solid-state fermentation (SSF) conditions. During SSF, the activity of lignolytic (laccase and manganese peroxidase) and hydrolytic (xylanase, cellulase, β-glucosidase, and invertase) enzymes was measured, with the activities of laccase (2.66 U/gdb in jars and 0.96 U/gdb in the bioreactor) and xylanase (346.04 U/gdb in jars and 200.65 U/gdb in the bioreactor) being the highest. The effect of the complex enzyme system was reflected in the changes in the chemical composition of GP with increasing ash, crude protein, and free fat content: 28%, 10%, and 17% in the laboratory jars, and 29%, 11%, and 7% in the bioreactor, respectively. In addition, the biological treatment improved the extractability of 13 individual phenolic compounds. Therefore, the applied SSF technique represents an effective strategy to improve the profile of phenolic compounds and the nutritional composition of GP, promoting their valorization and opening the door for potential applications in the food industry and other sectors.