We propose the use of green hydrogen as a fuel for a seawater heater in a humidification / dehumidification (HDH) desalination plant to increase its productivity, to allow scaling to large dimensions without negative environmental effects, and to guarantee continuous operation. We develop a mathematical model of the proposed HDH configuration. For operating conditions that guarantee very low NOX production, the fuel consumption is ~0.03 kg of H2 per kg of pure water produced. If the exhaust gases from the seawater heater are used for heat recovery, the GOR of the equipment may increase by up to 39 % in relation to the same equipment operating without heat recovery. The operation cost of freshwater is comparable to the costs obtained by other equipment in the literature. If the water produced in the combustion of hydrogen is condensed during the heat recovery process and then added to the freshwater produced, the production cost is reduced by 20 %. We found that an excess of air in the air+fuel mix beyond the minimum value appropriate for a low NOX generation does not provide significant benefits. The efficiency of the seawater heater has an impact on the production of pure water, but this impact is strongly mitigated by the heat recovery process. Fuel consumption increases proportionally with the decrease in the effectiveness of the heat recovery device, which is a key parameter for optimal performance. A hydrogen heater is also a good alternative as an auxiliary power source to guarantee continuous operation. On sunny hours a H2 heater may be used to increase productivity preheating the seawater, and at night the system could operate 100 % based on H2.