The origin of the Papua New Guinea tsunami that killed over 2100 people on 17 July 1998 has remained controversial, as dislocation sources based on the parent earthquake fail to model its extreme run–up amplitude. The generation of tsunamis by submarine mass failure had been considered a rare phenomenon which had aroused virtually no attention in terms of tsunami hazard mitigation. We report on recently acquired high–resolution seismic reflection data which yield new images of a large underwater slump, coincident with photographic and bathymetric evidence of the same feature, suspected of having generated the tsunami. T–phase records from an unblocked hydrophone at Wake Island provide new evidence for the timing of the slump. By merging geological data with hydrodynamic modelling, we reproduce the observed tsunami amplitude and timing in a manner consistent with eyewitness accounts. Submarine mass failure is predicted based on fundamental geological and geotechnical information.