The step, announced yesterday by the US Attorney-General, Janet Reno, is part of a new agreement on migration policy negotiated in New York by US and Cuban diplomats.
At the same time, the US will begin automatically repatriating Cubans intercepted at sea heading for American shores.
With summer approaching, there has been deepening concern in Washington both about security at Guantanamo and about the prospects of another outflow of refugees from Cuba. Last August, roughly 35,000 Cubans headed out to sea on boats and small rafts hoping for shelter in the US.
Meanwhile, the British government confirmed yesterday that it would allow the Cayman Islands, a British territory 200 miles south of Cuba, to turn back any Cubans. Last summer, the Caymans, a tax and tourism haven, received about 1,200 of the seaborne refugees. It housed them in a temporary camp where about 170 remain.
There are currently about 21,000 refugees trapped in Guantanamo. US officials said they expected roughly 15,000 to be granted refugee status on a case-by-case basis, while the remainder were likely to be rejected on grounds of health problems or criminal records.
Ms Reno insisted that receiving the Guantanamo refugees would not mean a net increase in the number of Cubans taken in by the US this year. Last September, the US agreed with Fidel Castro's government to increase to 20,000 the number of Cubans that would be allowed into the US annually. Those accepted from Guantanamo are to be set against that quota for this year.
While clearing Guantanamo of refugees is important for Washington - the camp was costing the Pentagon $1m a day and there have been constant worries about rioting - measures to discourage a fresh exodus were more urgent.
While promising to return any Cubans found at sea, the US won agreement from the Cuban authorities that they will accept back anyone who is repatriated and not punish them. "They will suffer no adverse consequences or reprisals of any sort," Ms Reno said.
Cuban representatives repeatedly warned that a bill introduced in the US Senate by Senator Jesse Helms to reinforce the US economic embargo against Cuba could alone provide the catalyst for a new refugee exodus. The bill is due to be debated later this month.
The new measures will get a mixed reception in Florida, home to the politically- influential Cuban-American community. Cuban leaders in Miami have been lobbying for months for asylum for those trapped at Guantanamo.
However, there will be anger at the decision to repatriate all those intercepted in future.