Accurate prediction of global sea-level rise requires that we understand the cause of recent, widespread and intensifying glacier acceleration along Antarctic ice-sheet coastal margins. Floating ice shelves buttress the flow of grounded tributary glaciers and their thickness and extent are particularly susceptible to changes in both climate and ocean forcing. Recent ice-shelf collapse led to retreat and acceleration of several glaciers on the Antarctic Peninsula. However, the extent and magnitude of ice-shelf thickness change, its causes and its link to glacier flow rate are so poorly understood that its influence on the future of the ice sheets cannot yet be predicted. Here we use satellite laser altimetry and modelling of the surface firn layer to reveal for the first time the circum-Antarctic pattern of ice-shelf thinning through increased basal melt. We deduce that this increased melt is the primary driver of Antarctic ice-sheet loss, through a reduction in buttressing of the adjacent ice sheet that has led to accelerated glacier flow. The highest thinning rates (~7 m/a) occur where warm water at depth can access thick ice shelves via submarine troughs crossing the continental shelf. Wind forcing could explain the dominant patterns of both basal melting and the surface melting and collapse of Antarctic ice shelves, through ocean upwelling in the Amundsen and Bellingshausen Seas and atmospheric warming on the Antarctic Peninsula. This implies that climate forcing through changing winds influences Antarctic Ice Sheet mass balance, and hence global sea-level, on annual to decadal timescales.