The repeal of the "wet foot, dry foot" policy is effective immediately, according the official. The decision follows months of negotiations focused in part on getting Cuba to agree to take back people who had arrived in the US.
The US and Cuba planned to issue a joint statement late Thursday. The official insisted on anonymity in order to detail the change ahead of the announcement.
The official yesterday said the Cubans gave no assurances about treatment of those sent back to the country, but said political asylum remains an option for those concerned about persecution if they return.
The "wet foot, dry foot" policy was put in place in 1995 by President Bill Clinton as a revision of a more liberal immigration policy. Until then, Cubans caught at sea trying to make their way to the United States were allowed into the country and were able to become legal residents after a year.
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The US was reluctant to send people back to the communist island then run by Fidel Castro, and the Cuban government also generally refused to accept repatriated citizens.
The changes would be the latest step by Obama to normalize relations with Cuba
Relations between the United States and Cuba were stuck in a Cold War freeze for decades, but Obama and Cuban President Raul Castro established full diplomatic ties and opened embassies in their capitals in 2015. Obama visited Havana last March.
The official also cited an uptick in Cuban migration, particularly across the US-Mexico border an increase the official said reflected an expectation among Cubans that the Obama administration would soon move to end their special immigration status.
The Cuban Medical Professional Parole Program, which was started by President George W Bush in 2006, is also being rescinded. The measure allowed Cuban doctors, nurses and other medical professionals to seek parole in the US while on assignments abroad.