It took about 2 hours for the first tsunami to hit.
http://www.cnn.com/SPECIALS/2004/tsunami.disaster/
12:59 a.m. GMT Sunday
A huge earthquake erupted in the Indian Ocean off Sumatra, Indonesia.
1:07 a.m. GMT
Seismic signals from stations in Australia alerted the NOAA Pacific Tsunami Warning Center in Hawaii about an earthquake.
1:14 a.m. GMT
The tsunami warning center in Hawaii sent a bulletin to nations that participate in the Tsunami Warning System in the Pacific (ITSU). India, Sri Lanka and the Maldives are not members of the system.
2:04 a.m. GMT
A second bulletin was sent, alerting nations that the earthquake had a preliminary magnitude of 8.5. The bulletin said the ITSU nations did not face the threat of a tsunami, but did cite the possibility of a tsunami near the quake's epicenter.
2:30 a.m. GMT
The warning center alerted the Australia Management System.
3:30 a.m. GMT
The center received the first indications that devastating tsunamis had formed from Internet news reports of casualties in Sri Lanka. It's believed the deadly waves had struck the whole region by then.
If I remember correctly, it took two hours.