They met with a team of three from the International Red Cross, and a doctor gave all four hostages a medical check. Only one required medicine, but was not seriously ill.
According to a spokesman, the International Committee of the Red Cross will be speaking to parents of all the hostages today. The Red Cross team was given letters for the parents and some photographs of the hostages. The four British hostages are Annette van der Kolk, Ann McIvor, Daniel Stark and William Oates.
"In general they are in good condition, although some of them have lost weight because of the gruelling time in captivity," said Jorg Stocklin, an ICRC spokesman in Geneva. None was in critical condition, including pregnant Dutchwoman Martha Klein, 32, he said. She had been reported to have been suffering from malaria and malnutrition.
"We cannot divulge the details of the health condition of the hostages because we will inform their families individually," Mr Stocklin said. He described the meeting with the hostages as an emotional one, "since it was the first time they met anybody from outside".
He said they were taken blankets, food and medicine provided by the Indonesian government and the embassies of Britain and the Netherlands.
The Red Cross went to Irian Jaya, following requests by the rebels and approval by the Indonesian armed forces, to mediate in the hostages' release.
Insurgents of the Free Papua Movement have been fighting for the independence of Irian Jaya, a former Dutch colony ceded to Indonesia in 1963.
It is understood that the OPM, the freedom movement for West Papua, is insisting it will only consider the release of the hostages to an international agency because it disputes Indonesian jurisdiction.
Irian Jaya is home to 250 tribes making up some one million inhabitants. They live in jungle long-houses, in tree-top buildings and in homes built on stilts along the coast.
The Red Cross team had been in the mountain town of Wamena for two weeks while they carefully negotiated with the army for free access to the hostages. They were afraid military operations might have been launched at the same time in the area.
When the Catholic bishop, Monsignor H F Munninghoff went to meet the leader of the kidnappers, Kelly Kwalik, the army followed a day later with an undercover team. This time, the army has promised not to take advantage of the visit.
The hostages are reported to be weak due to constant movement from one village to another.
Latest reports say that they are living in a mountain cave - not far from the massive RTZ Freeport gold mine where Rio Tinto Zinc is now investing $1.7bn in further expansion.
The operation of this mine is a key issue with the kidnappers. In 1977, Kwalik led an attack on the mine, blowing up a pipeline taking the ore to the coast. In a counter-offensive by the Indonesian army, several thousands tribespeople were reported killed.
The mine is the biggest British investment in South-East Asia. It is the world's biggest gold mine and the third-biggest copper mine. As part of its contract with the government, it provides living and transport facilities for the Indonesian Army.
According to Tim Wirth, the US Under-Secretary of State for Global Affairs: "The Indonesian government have not done much to establish a government there and Freeport therefore has become in many ways both company and government."
The hostages were seized on 8 January at a meeting in Mapnduma, a village in the mountains, to discuss the creation of a major national park. Some tribespeople at the meeting saw the national park as a way of securing income but others saw it as an alienation of their tribal lands.
Daniel Kogowa, a leader of the OPM, strongly objected. That afternoon, the 26 hostages were taken. Since then, 14 hostages have been released. The British hostages were on a scientific expedition to the area paid for by BP, and were all from Cambridge University.
The British and Dutch military attaches are in Wamena and will be briefed by the Red Cross today on the meeting with the rebels.