This study demonstrates the application of hollow-fiber membrane contactors (HFMCs) for the recovery of biogas from the ultrafiltration permeate of an anaerobic membrane bioreactor (AnMBR) and synthetic effluents of pure and mixed CH4 and CO2. The developed membrane degassing setup was coupled with a pilot-scale AnMBR fed with synthetic domestic effluent working at 25 °C. The membrane degassing unit was able to recover 93% of the total dissolved CH4 and 83% of the dissolved CO2 in the first two hours of permeate recirculation. The initial recovery rates were very high (0.21 mg CH4 L−1 min−1 and 8.43 mg CO2 L−1 min−1) and the membrane was able to achieve a degassing efficiency of 95.7% for CH4 and 76.2% for CO2, at a gas to liquid ratio of 1. A higher mass transfer coefficient of CH4 was found in all experimental and theoretical evaluations compared to CO2. This could also be confirmed from the higher transmembrane mass transport resistance to CO2 rather than CH4 found in this work. A strong dependency of the selective gas transport on the gas and liquid side hydrodynamics was observed. An increase in the liquid flow rate and gas flow rate favored CH4 transport and CO2 transport, respectively, over each component. The results confirmed the effectiveness of the collective AnMBR and membrane degassing setup for biogas recovery. Still, additional work is required to improve the membrane contactor’s performance for biogas recovery during long-term operation.