The tsunami caused by the Great Sumatra Earthquake on 26 December 2004 generated dispersive signals recorded on hydrophones near Diego Garcia and Cape Leeuwin, Australia and on seismographs in coastal locations around the Indian Ocean. The onset of these signals was coincident with predicted tsunami arrival times, signal durations were from 12 to more than 36 hours, and signal frequencies ranged from less than 1 mHz at onset to 25 mHz. Signal onset times and dispersion are consistent with propagation from the earthquake rupture zone to the receivers as tsunami waves. Signal arrival azimuths were estimated from coherent processing of groups of sensors. The azimuth and dispersion of the signal are consistent with the direct tsunami wave, and secondary signals are consistent with reflections of the tsunami from the Mascarene Plateau and other bathymetric features in the Indian Ocean.