The decision was taken following discussions between Prime Minister Tony Blair -- currently on holiday in Egypt -- and government ministers, a Downing Street spokeswoman said.
Royal Fleet Auxiliary Diligence, a repair ship carrying 38 crew, and frigate HMS Chatham, with around 170 crew, were expected to arrive in the affected area on January 4.
"They will provide a range of capabilities to assist in disaster relief, including Chatham's Lynx helicopters," the spokeswoman said.
Their precise destination had yet to be decided, but was likely to be either Sri Lanka or the Maldives, she added. A Royal Air Force C-17 cargo plane will also be sent to the region to assist with relief efforts.
According to the Ministry of Defence, HMS Chatham is currently sailing east from Dubai, while the repair ship is off the coast of India.
Aid workers have warned that a rapid international response is needed to help survivors of Sunday's massive sea surges, which killed more than 125,000 people around the Indian Ocean region.
The British government on Thursday more than tripled its own pledge for aid to the tsunami disaster to 50 million pounds (96 million dollars, 70.5 million euros), the biggest single donation by a national government.