This paper analyzes the use of hybrid photovoltaic/thermal (PVT) collectors in nearly zero-energy buildings (NZEBs). We present a design methodology based on the dynamic simulation of the whole energy system, which includes the building energy demand, a reversible heat pump as generator, the thermal storage, the power exchange with the grid, and both thermal and electrical energy production by solar collectors. An exhaustive search of the best equipment sizing and design is performed to minimize both the total costs and the non-renewable primary energy consumption over the system lifetime. The results show that photovoltaic/thermal technology reduces the non-renewable primary energy consumption below the nearly zero-energy threshold value, assumed as 15 kWh/(m2 yr), also reducing the total costs with respect to a non-solar solution (up to 8%). As expected, several possible optimal designs exist, with an opposite trend between energy savings and total costs. In all these optimal configurations, we figure out that photovoltaic/thermal technology favors the production of electrical energy with respect to the thermal one, which mainly occurs during the summer to meet the domestic hot water requirements and lower the temperature of the collectors. Finally, we show that, for a given solar area, photovoltaic/thermal technology leads to a higher reduction of the non-renewable primary energy and to a higher production of solar thermal energy with respect to a traditional separate production employing photovoltaic (PV) modules and solar thermal (ST) collectors.