Solid oxide fuel cell (SOFC)–gas turbine (GT) hybrid systems can produce power at high electrical efficiencies while emitting virtually zero criteria pollutants (e.g., ozone, carbon monoxide, oxides of nitrogen and sulfur, and particulate matters). This study presents new insights into renewable hydrogen (RH2)-powered SOFC–GT hybrid systems with respect to their system configuration and techno-economic analysis motivated by the need for clean on-demand power. First, three system configurations are thermodynamically assessed: (I) a reference case with no SOFC off-gas recirculation, (II) a case with cathode off-gas recirculation, and (III) a case with anode off-gas recirculation. While these configurations have been studied in isolation, here we provide a detailed performance comparison. Moreover, a techno-economic analysis is conducted to study the economic competitiveness of RH2-fueled hybrid systems and the economies of scale by offering a comparison to natural gas (NG)-fueled systems. Results show that the case with anode off-gas recirculation, with 68.50%-lower heating value (LHV) at a 10 MW scale, has the highest efficiency among the studied scenarios. When moving from 10 MW to 50 MW, the efficiency increases to 70.22%-LHV. These high efficiency values make SOFC–GT hybrid systems highly attractive in the context of a circular economy as they outcompete most other power generation technologies. The cost-of-electricity (COE) is reduced by about 10% when moving from 10 MW to 50 MW, from USD 1976/kW to USD 1668/kW, respectively. Renewable H2 is expected to be economically competitive with NG by 2030, when the U.S. Department of Energy’s target of USD 1/kg RH2 is reached.