Satellite observations over the past two decades have revealed increasing loss of grounded ice in West Antarctica, associated with floating ice shelves that have been thinning. Thinning reduces an ice shelf’s ability to restrain grounded-ice discharge, yet our understanding of the climate processes that drive mass changes is limited. Here, we use ice-shelf height data from four satellite altimeter missions (1994–2017) to show a direct link between ice-shelf height variability in the Antarctic Pacific sector and changes in regional atmospheric circulation driven by the El Niño/Southern Oscillation. This link is strongest from the Dotson to Ross ice shelves and weaker elsewhere. During intense El Niño years, height increase by accumulation exceeds the height decrease by basal melting, but net ice-shelf mass declines as basal ice loss exceeds ice gain by lower-density snow. Our results demonstrate a substantial response of Amundsen Sea ice shelves to global and regional climate variability, with rates of change in height and mass on interannual timescales that can be comparable to the longer-term trend, and with mass changes from surface accumulation offsetting a significant fraction of the changes in basal melting. This implies that ice-shelf height and mass variability will increase as interannual atmospheric variability increases in a warming climate.