Last year a US federal judge ordered the men released into the US but an appeals court halted the order, and they have been in legal limbo ever since.
The US state department has said the Uighurs cannot be returned to China, despite requests from Beijing that they be handed over, because of fears they will face persecution and possible execution.
Instead US officials have been trying to find a third country willing to take them in, but in the meantime they have been kept in Guantanamo, spending up to 22 hours a day locked in their cells.
Beijing reiterated its claim on Thursday that the 17 Chinese Muslims are terrorists and should be handed back to China.
"Growing up under communism we always dreamed of living in peace and working in free society like this one [in Bermuda]"
Abdul Nasser, Uighur former detainee
Ewart Brown, Bermuda's leader, said on Thursday that the US had agreed to bear the costs associated with relocating the men on the island.
In a statement, Brown said the men have "the opportunity to become naturalised citizens and thereafter afforded the right to travel and leave Bermuda, potentially settling elsewhere."
The premier also said he felt a responsibility to help the men "who have been caught in a web of reaction to tragic events which at the time of their happening were not well understood".
Abdul Nasser, one of the four detainees who landed in Bermuda early on Thursday, issued a statement through his lawyers, saying: "Growing up under communism we always dreamed of living in peace and working in free society like this one. Today you have let freedom ring."
On Wednesday Johnson Toribiong, the Palau president, said his country was "honoured and proud that the United States has asked Palau to assist with such a critical task".
"Palau's accommodation to accept the temporary resettlement of these detainees is a humanitarian gesture intended to help them be freed of any further unnecessary incarceration and to restart their lives in as normal a fashion as possible," he said.
Toribiong said Palau officials would travel to review the situation at Guantanamo Bay, which Barack Obama, the US president, has said he intends to close.
Palau, with a population estimated at about 21,000 is one of the world's smallest and youngest countries having gained its independence in October 1994.
|Obama wants to close the facility at
Guantanamo by next year [AFP]
In 2006 Albania agreed to accept five Uighur detainees from Guantanamo, but has said it will not take others due to fears of possible diplomatic repercussions from China, one of its main trading partners and investors.
Germany had been considered a possible destination as it has a large Uighur community, but no agreement was reached.
Last month two US congressmen called for the Uighur men to be allowed to resettle within the Uighur community in the US, saying that their continued detention without trial and after being cleared of any wrongdoing was an injustice.
Uighurs are mostly Turkic-speaking and Muslim, and many say they have long been repressed by the Chinese government.
China says Uighur nationalists are leading a separatist movement in the country's western Xinjiang region and are responsible for a series of terrorist attacks.