Story highlights Havana has argued the policy encourages Cubans to make the dangerous trip to the US

The decision was likely Obama's last move in his historic dealings with Cuba

Washington (CNN) President Barack Obama is ending the longstanding "wet foot, dry foot" policy that allows Cubans who arrive in the United States without a visa to become permanent residents, the administration announced Thursday.

The move, which wasn't previously outlined and is likely one of the final foreign policy decisions of Obama's term, terminates a decades-long policy that many argued amounted to preferential treatment for a single group of migrants.

"By taking this step, we are treating Cuban migrants the same way we treat migrants from other countries," Obama wrote in a statement Thursday.

"The United States, a land of immigrants, has been enriched by the contributions of Cuban-Americans for more than a century," he continued. "Since I took office, we have put the Cuban-American community at the center of our policies. With this change we will continue to welcome Cubans as we welcome immigrants from other nations, consistent with our laws."

The policy, in place for more than two decades, had applied solely to Cubans. Following a mass exodus of Cubans to the United States, former President Bill Clinton in the mid-1990s changed the "open door" policy on Cuban refugees -- first established by President Lyndon B. Johnson -- to the "wet, foot, dry foot" policy that repatriated Cubans intercepted at sea but allowed those who reach land to stay.

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