President Barack Obama announced Thursday that he was ending a longstanding immigration policy that allowed any Cuban who made it to U.S. soil to stay and become a legal resident.

In a statement, Obama said the so-called "wet foot, dry foot" policy was "designed for a different era" of U.S.-Cuba relations.

Under the new policy, which takes effect immediately, Cubans who attempt to enter the U.S. illegally without qualifying for humanitarian relief will be sent back to the island.

"By taking this step," Obama said, "we are treating Cuban migrants the same way we treat migrants from other countries."

Obama added that the Havana government had agreed to accept Cubans ordered to leave the U.S., a concession that was a focus of months of negotiations. A senior administration official told the Associated Press 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.

Homeland Security Secretary Jeh Johnson said the move "goes a long way to putting our relationship with Cuba on equal terms with our relationships with other neighbors."

Obama is using an administrative rule change to end the policy. President-elect Donald Trump could undo that rule after he is sworn in next week. He has criticized Obama's moves to improve relations with Cuba. But ending a policy that has allowed hundreds of thousands of people to come to the United States without a visa also aligns with Trump's commitment to tough immigration policies.

The "wet foot, dry foot" policy was put in place in 1995 by then-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. The U.S. 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 Cuban government has in the past complained bitterly about the special immigration privileges, saying they encourage Cubans to risk dangerous escape trips and drain the country of professionals. But it has also served as a release valve for the single-party state, allowing the most dissatisfied Cubans to seek better lives outside and become sources of financial support for relatives on the island.

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.

U.S. and Cuban officials were meeting Thursday in Washington to coordinate efforts to fight human trafficking. A decades-old U.S. economic embargo, though, remains in place as does the Cuban Adjustment Act which lets Cubans become permanent residents a year after legally arriving in the U.S.

The official said that in recent years, most people fleeing the island have done so for economic reasons or to take advantage of the benefits they know they can receive if they make it to the U.S.

The official also cited an uptick in Cuban migration, particularly across the U.S.-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.

Since October 2012, more than 118,000 Cubans have presented themselves at ports of entry along the border, according to statistics published by the Homeland Security Department. During the 2016 budget year, which ended in September, a five-year high of more than 41,500 people came through the southern border. An additional 7,000 people arrived between October and November.

The influx has created burdens on other countries in the region that must contend with Cubans who have yet to reach the U.S. border, the official said.

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 U.S. while on assignments abroad.

People already in the pipeline under both "wet foot, dry foot" and the medical parole program will be able to continue the process toward getting legal status.

The preferential treatment for Cubans reflected the political power of Cuban-Americans, especially in Florida, a critical state in presidential elections. That has been shifting in recent years. Older Cubans, particularly those who fled Castro's regime, tend to reject Obama's diplomatic overtures to Cuba. Younger Cuban-American voters have proven less likely than their parents and grandparents to define their politics by U.S.-Cuba relations. Exit polls show President Barack Obama managed roughly a split in the Florida Cuban vote in 2012, and Trump in November won the same group by a much narrower margin than many previous Republican nominees.

The Associated Press contributed to this report.