During storage, elevated temperature and humidity cause accelerated aging and deterioration of seeds of various plant species, including important cultivated cereals, such as wheat and triticale. Germination of old seeds can be facilitated by seed priming with physiologically active substances that correct the pro/antioxidant balance and reduce the development of oxidative stress. Gamma-aminobutyric acid (GABA) is a regulatory compound with direct and indirect antioxidant effects. However, its effect on the germination of grains of cereals with low germination has not been extensively studied. The objective of this study was to examine the impact of GABA priming on the germination of aged grains of winter bread wheat (Triticum aestivum ‘Scorpion’) and winter triticale (×Triticosecale ‘Raritet’). the extent of oxidative stress and the state of the antioxidant system in seedlings. The results indicated that a three-hour treatment of grains with GABA at the optimal concentration (1 mM) resulted in a significant (18–21%) increase in germination energy and seed germination rate, as well as an increase in the biomass of shoots and roots of seedlings of both species. Concomitantly, the influence of GABA resulted in a reduction in oxidative stress markers, including the generation of superoxide anion radicals, hydrogen peroxide content, and the product of lipid peroxidation malondialdehyde. In wheat seedlings, the total content of phenolic compounds increased, while in triticale seedlings, the content of anthocyanins increased almost twofold. In seedlings derived from GABA-primed grains, catalase activity was also significantly elevated in the absence of notable alterations in superoxide dismutase and peroxidase activity. It was postulated that GABA priming is a promising approach for enhancing the germination of cereal seeds with diminished sowing quality.