An attractive way toward a more rational conversion of fuel and biofuel is the decentralized power generation and cogeneration. The fuel cell-gas turbine hybrid cycles are emerging as the most promising candidates to achieve in decentralized generation comparable or higher efficiency than in large scale power plants. The present contribution is devoted to the design and optimization of an innovative concept of small scale Solid Oxide Fuel Cell – Gas Turbine hybrid cycle for residential applications. A 5kW planar SOFC module, operating at atmospheric pressure, is integrated with a micro gas turbine unit, including two radial turbines and one radial compressor, based on an inverted Brayton cycle. A thermodynamic optimization approach, coupled with system energy integration, is applied to evaluate several design options. The optimization results indicate the existence of realistic optimal designs achieving exergy efficiency higher than 66%. Sensitivity analyses on the more sensible parameters are carried out. The heat exchanger network definition is performed for an optimal configuration and a system layout is proposed. The cogeneration performance of the system and its integration in common residential buildings are discussed.