The El Niño-Southern Oscillation (ENSO) influences climate variability globally, encompassing various other modes of variability, and thus represents a key predictable climate signal on seasonal timescales. Yet, its response to greenhouse warming remains uncertain, with models projecting a range of outcomes. Here, we demonstrate that in response to warming, a state-of-the-art high-resolution climate model simulates a rapid transition from a moderate-amplitude irregular regime, as observed in the current climate, to a highly regular oscillation with intensifying amplitude. This behaviour can be attributed to increasing air-sea feedbacks, which approach criticality in the second half of this century, and growing atmospheric noise. As ENSO intensifies in this model, it synchronizes with other prominent climate modes, such as the North Atlantic Oscillation and the Indian Ocean Dipole, thereby imprinting its regular, predictable variability on them. If realized, this global climate mode resonance would have wide-ranging whiplash impacts on regional hydroclimates.