Rapid sea-level rise caused by the collapse of large ice sheets is a global threat to human societies. In the last deglacial period, the rate of global sea-level rise peaked at more than 4 cm/yr during Meltwater Pulse 1a, which coincided with the abrupt Bølling warming event 14,650 yr ago. However, the sources of the meltwater have proven elusive, and the contribution from Eurasian ice sheets has until now been considered negligible. Here we show that marine-based sectors of the Eurasian ice sheet complex collapsed at the Bølling transition and lost an ice volume of between 4.5 and 7.9 m sea level equivalents (95\% quantiles) over 500 yr. During peak melting 14,650 - 14,310 yr ago, Eurasian ice sheets lost between 3.3 and 6.7 m sea level equivalents (95\% quantiles), thus contributing significantly to Meltwater Pulse 1a. A mean meltwater flux of 0.2 Sv over 300 yr was injected into the Norwegian Sea and the Arctic Ocean during a time when proxy evidence suggests vigorous Atlantic meridional overturning circulation. Our reconstruction of the EIS deglaciation shows that a marine-based ice sheet comparable in size to the West Antarctic ice sheet can collapse in as little as 300-500 years.