The measure will now go to President Barack Obama for his signature.
The vote came hours after the US supreme court ruled that it will hear an appeal by Chinese Muslim Uighurs imprisoned at Guantanamo.
The court agreed to decide whether US federal judges are allowed to order the government to release Guantanamo prisoners into the US when no other country will take them.
The decision to hear the case comes after a US appeals court ruled that only the executive branch can decide whether to allow Uighurs into the US.
The decision by America's highest court to hear the case comes after the Obama administration had called for it to be rejected.
The appeals court overturned a ruling made a year ago by a federal judge that 17 Uighurs jailed at Guantanamo since 2002 should be immediately released into the US.
Resettlement
US authorities have said that the Uighurs are no longer suspected of any role in terrorist attacks or plots, but the US government has said it cannot return the Uighurs to China due to fears that they would be persecuted.
Four of the Uighurs were resettled in Bermuda in June, and Elena Kagan, the US solicitor-general, told the US supreme court in September that Palau had agreed to take 12 of the 13 remaining Uighurs.
Six Uighurs have agreed to be resettled in Palau, she said, adding that two more may soon agree to go.
The US government was trying to find a place to send the others, she said.
Obama has ordered that the prison at Guantanamo be shut down by January 22, but there have been a host of legal and political obstacles which mean that the date is unlikely to be met, according to administration officials.
The Obama administration said earlier this year that it was considering releasing the Uighurs held at Guantanamo in the US, but the idea faced widespread congressional opposition.
The US congress is now considering legislation that would allow Guantanamo prisoners into the US only to face trial.