The approximately 10,000-year-long Last Glacial Maximum, before the termination of the last ice age, was the coldest period in Earth's recent climate history1. Relative to the Holocene epoch, atmospheric carbon dioxide was about 100 parts per million lower and tropical sea surface temperatures were about 3 to 5 degrees Celsius lower2,3. The Last Glacial Maximum began when global mean sea level (GMSL) abruptly dropped by about 40 metres around 31,000 years ago4 and was followed by about 10,000 years of rapid deglaciation into the Holocene1. The masses of the melting polar ice sheets and the change in ocean volume, and hence in GMSL, are primary constraints for climate models constructed to describe the transition between the Last Glacial Maximum and the Holocene, and future changes; but the rate, timing and magnitude of this transition remain uncertain. Here we show that sea level at the shelf edge of the Great Barrier Reef dropped by around 20 metres between 21,900 and 20,500 years ago, to -118 metres relative to the modern level. Our findings are based on recovered and radiometrically dated fossil corals and coralline algae assemblages, and represent relative sea level at the Great Barrier Reef, rather than GMSL. Subsequently, relative sea level rose at a rate of about 3.5 millimetres per year for around 4,000 years. The rise is consistent with the warming previously observed at 19,000 years ago1,5, but we now show that it occurred just after the 20-metre drop in relative sea level and the related increase in global ice volumes. The detailed structure of our record is robust because the Great Barrier Reef is remote from former ice sheets and tectonic activity. Relative sea level can be influenced by Earth's response to regional changes in ice and water loadings and may differ greatly from GMSL. Consequently, we used glacio-isostatic models to derive GMSL, and find that the Last Glacial Maximum culminated 20,500 years ago in a GMSL low of about -125 to -130 metres.