When nuclear waste is immobilized in cement or geopolymer, gases may be generated by corrosion and radiolysis. This production must be accurately predicted, and waste loading and countermeasures selected accordingly to avoid overpressure and limit the risk of explosion in the case of dihydrogen (H2). We measured and simulated H2 generation and release from water-saturated geopolymer confined in a glass bottle under 60Co gamma irradiation. It was observed that confinement of H2 in the pores of a high pH geopolymer could lead to recombination of more than 99.9 % of the hydrogen generated by radiolysis. Shrinkage can allow hydrogen to diffuse between the geopolymer and the vessel, reducing the fraction of recombined H2 to 90 % at our experimental scale. We then used a model to scale up the results of our experiments. The hydrogen release of a saturated geopolymer in a standard 200 L drum is expected to be equivalent to that of a hydraulic binder containing approximately 2 % moisture. Harnessing the effects of recombination would make it possible to preserve the capacity of countermeasures such as H2 absorbers, increase the loading capacity of waste packages, and reduce the cost of nuclear waste immobilization.