Seafloor methane release due to the thermal dissociation of gas hydrates is pervasive across the continental margins of the Arctic Ocean. Furthermore, there is increasing awareness that shallow hydrate-related methane seeps have appeared due to enhanced warming of Arctic Ocean bottom water during the last century. Although it has been argued that a gas hydrate gun could trigger abrupt climate change, the processes and rates of subsurface/atmospheric natural gas exchange remain uncertain. Here we investigate the dynamics between gas hydrate stability and environmental changes from the height of the last glaciation through to the present day. Using geophysical observations from offshore Svalbard to constrain a coupled ice sheet/gas hydrate model, we identify distinct phases of subglacial methane sequestration and subsequent release on ice sheet retreat that led to the formation of a suite of seafloor domes. Reconstructing the evolution of this dome field, we find that incursions of warm Atlantic bottom water forced rapid gas hydrate dissociation and enhanced methane emissions during the penultimate Heinrich event, the Bølling and Allerød interstadials, and the Holocene optimum. Our results highlight the complex interplay between the cryosphere, geosphere, and atmosphere over the last 30,000 y that led to extensive changes in subseafloor carbon storage that forced distinct episodes of methane release due to natural climate variability well before recent anthropogenic warming.