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WASHINGTON — The Obama administration on Thursday will terminate the so-called wet foot, dry foot policy that allows Cubans who arrive on United States soil without visas to remain in the country and gain legal residency, a senior administration official said, in an unexpected move long sought by the Cuban government.

The action, first reported by The Associated Press, will come through a new Department of Homeland Security regulation and an agreement with the Cuban government. Details of the decision were disclosed on the condition of anonymity to avoid pre-empting a formal announcement expected later Thursday.

The Obama administration had long insisted it was not planning to change the policy after President Obama’s move in 2014 toward normalized relations with Cuba. But the thaw prompted speculation that once diplomatic relations resumed, as they did in 2015, the arrangement would end.

Under the current policy, Cubans detained at sea who are trying to reach the United States must return to their country, but those who make it onto American soil are allowed to stay and eventually apply for legal permanent residency. The unusual arrangement has been unique to Cuban refugees.

Federal figures show that at least 63,000 Cubans moved to the United States last year, the bulk of them crossing the southwestern border on foot. More than 250,000 Cubans have been granted residency during the Obama administration.