The El Niño-Southern Oscillation (ENSO) is the dominant and most consequential climate variation on Earth, and is characterized by warming of equatorial Pacific sea surface temperatures (SSTs) during the El Niño phase and cooling during the La Niña phase. ENSO events tend to have a centre-corresponding to the location of the maximum SST anomaly-in either the central equatorial Pacific (5° S-5° N, 160° E-150° W) or the eastern equatorial Pacific (5° S-5° N, 150°-90° W); these two distinct types of ENSO event are referred to as the CP-ENSO and EP-ENSO regimes, respectively. How the ENSO may change under future greenhouse warming is unknown, owing to a lack of inter-model agreement over the response of SSTs in the eastern equatorial Pacific to such warming. Here we find a robust increase in future EP-ENSO SST variability among CMIP5 climate models that simulate the two distinct ENSO regimes. We show that the EP-ENSO SST anomaly pattern and its centre differ greatly from one model to another, and therefore cannot be well represented by a single SST 'index' at the observed centre. However, although the locations of the anomaly centres differ in each model, we find a robust increase in SST variability at each anomaly centre across the majority of models considered. This increase in variability is largely due to greenhouse-warming-induced intensification of upper-ocean stratification in the equatorial Pacific, which enhances ocean-atmosphere coupling. An increase in SST variance implies an increase in the number of 'strong' EP-El Niño events (corresponding to large SST anomalies) and associated extreme weather events.