Iceland and the entire Northeast Atlantic around it are characterised by abundant intraplate volcanism, anomalously high topography and, in many places, anomalously thick basaltic crust. This has been attributed to the hot Iceland Plume rising from the deep mantle, but the structure and the very existence of the plume are debated. Using seismic waveform tomography with very large datasets, including abundant, recently collected data in the region, we image a large, low-velocity body located beneath central-eastern Greenland in the mantle transition zone (410-660 km depth) and rising, upwards and eastwards, to below Iceland near the surface. We interpret this body as the Iceland plume, ascending from under Greenland and captured by the Mid-Atlantic Ridge. The ascent of the plume beneath the western part of the Northeast Atlantic is consistent with the thinner lithosphere there, as revealed by our tomography, and much more abundant seamounts, compared to the eastern part of the basin.