Biogas is a renewable and promising alternative energy source produced by anaerobic digestion (AD) of organic wastes like animal, vegetable, kitchen, municipal solid, wastewater, and agriculture residue. At small and medium scales, biogas energy is frequently used to generate heat and electricity using turbines and internal combustion engines; however, the efficiency of these systems is very low compared to solid oxide fuel cell (SOFC) systems. The high-temperature operation and direct internal reforming of SOFC make it possible to use biogas to generate electricity via electrochemical redox reactions. This study developed a thermodynamic model of a 10-kW biogas-SOFC system for decentralised combined heat and power applications. The direct internal reforming SOFC with anode off-gas recirculation has been chosen for this system modelling. Energy and exergy analysis followed with techno-economic evaluation were conducted for the designed system model. The SOFC performance is also examined using sensitivity analysis to account for fuel utilisation and recirculation ratio variations. The biogas-fuelled SOFC system yields a net electrical efficiency of 66.81% and combined heat and power (CHP) efficiency of 76.03%. In terms of exergy efficiencies, the system has a net electrical efficiency of 63.76% and a CHP efficiency of 66.23%. The energy and exergy analysis reveal that the system has maximum efficiency with 85% fuel utilisation and 70% anode off-gas recirculation. The techno-economic study of the biogas-SOFC system shows the levelized cost of electricity (LCOE) as $0.20/kWh, comparable to conventional energy systems. This proves that the system is a feasible energy solution for decentralised power applications.