The access to the offshore wind resource in the deep sea requires the development of innovative solutions which reduce the cost of energy. Novel technologies propose the hybrid combination of wind and wave energy to improve the synergy between these technologies sharing costs, such as mooring and electrical connexion. This work proposes a novel hybrid wind and wave energy system integrating a floating offshore wind turbine with three-point absorbers wave energy converters (WECs). The WECs are an integral part of the floating structure and contribute significantly to the hydrostatic and dynamic stability of the system. Their geometry is optimised considering a cylindrical, semi-cylindrical and spherical shape for the Pantelleria case study. The cylindrical shape with the largest radius and the lowest height is the optimal solution in terms of reducing structural costs and maximising the performance of the WECs. The in-house hydrostatic stability tool and the time domain model MOST are used to optimise the WECs, with a combined meta-heuristic genetic algorithm with the Kriging surrogate model and a local Nelder–Mead optimization in the final simulations. The power of the WECs is estimated with both linear and variable motor flow hydraulic PTOs to obtain a more realistic electrical power generation. Generally, the hybrid device proved to be more competitive than the floating wind turbine alone, with a LCOE reduction up to 11%. Performance of the hybrid device can be further improved when more energetic sites are considered, as the energy generated by the WECs is higher.