Proxy-based indicators of past climate change show that current global climate models systematically underestimate Holocene-epoch climate variability on centennial to multi-millennial timescales, with the mismatch increasing for longer periods. Proposed explanations for the discrepancy include ocean-atmosphere coupling that is too weak in models, insufficient energy cascades from smaller to larger spatial and temporal scales, or that global climate models do not consider slow climate feedbacks related to the carbon cycle or interactions between ice sheets and climate. Such interactions, however, are known to have strongly affected centennial- to orbital-scale climate variability during past glaciations, and are likely to be important in future climate change. Here we show that fluctuations in Antarctic Ice Sheet discharge caused by relatively small changes in subsurface ocean temperature can amplify multi-centennial climate variability regionally and globally, suggesting that a dynamic Antarctic Ice Sheet may have driven climate fluctuations during the Holocene. We analysed high-temporal-resolution records of iceberg-rafted debris derived from the Antarctic Ice Sheet, and performed both high-spatial-resolution ice-sheet modelling of the Antarctic Ice Sheet and multi-millennial global climate model simulations. Ice-sheet responses to decadal-scale ocean forcing appear to be less important, possibly indicating that the future response of the Antarctic Ice Sheet will be governed more by long-term anthropogenic warming combined with multi-centennial natural variability than by annual or decadal climate oscillations.