Tsunami source of the 2004 Sumatra–Andaman earthquake was estimated from a joint inversion of tsunami waveforms recorded on tide gauges and sea surface heights captured by satellite altimetry measurements. The earthquake, the largest in the past 40 years, caused devastating tsunami damage to countries around the Indian Ocean, but the tsunami source, in particular, its northern end, was not well resolved. Although aftershocks and crustal deformation extended from off northwestern Sumatra Island through the Nicobar Islands to the Andaman Islands, some seismic-wave analyses indicated a shorter source length, several hundred kilometers. We used tsunami waveforms recorded at 12 tide gauge stations around the source and the sea surface heights measured by three satellites: Jason1, topex/Poseidon, and Envisat. We numerically computed tsunami propagation using realistic bathymetry; more than 66,000 depth points were digitized from nautical charts and combined with the ETOPO2 data. Inversion of satellite data indicates that the tsunami source extended to the Andaman Islands with a total length of 1,400 km, but such a model produces much larger tsunami waveforms than observed at Indian tide gauge stations. Inversion of tide gauge records and the joint inversion indicate that the tsunami source was about 900 km long. The largest slip, about 13 to 25 m, was located off Sumatra Island and the second largest slip, up to 7 m, near the Nicobar Islands. The slip distribution is similar for different rupture velocities and rise times, with a slow velocity of 1 km/sec and a rise time of 3 min yielding the largest variance reduction.