WASHINGTON—The U.S. and Cuba have reached an agreement to restore diplomatic relations and reopen embassies in each other's capitals, a senior Obama administration official said Tuesday, the biggest step yet toward ending a half century of animosity between the two countries.

President Barack Obama on Wednesday will announce the U.S. plan to reopen its embassy in Havana, the official said. Secretary of State John Kerry also was to address the move to convert the U.S. diplomatic post there into a full-fledged embassy.

Officials at the Cuban Interest Section in Washington didn't respond to a request for comment.

Cuba was formally removed from Washington's list of sponsors of state terrorism in late May, a critical step toward restoring diplomatic ties.

U.S. and Cuban leaders had announced in December they'd move to normalize relations. They held four rounds of talks to re-establish diplomatic ties, with the last meeting in Washington in May.

Obama administration officials see the re-establishment of diplomatic ties as the first step in a longer normalization process. Congress would need to act to fully remove an embargo on trade and travel, though Mr. Obama took steps to loosen restrictions in December.

The State Department must formally notify Congress of its intent to reopen the embassy in Havana. Congress then has 15 days to review the notification before the U.S. can go ahead and formally do so.

U.S. officials have said that the formal announcement of the reopening of the embassy and the notice to Congress would come together.

Ted Piccone, a Cuba expert at the Brookings Institution, said Wednesday's expected announcement is the most concrete development yet to come out of the policy shift. While Mr. Obama has taken several unilateral steps to advance warmer ties, including lifting Cuba from the terrorism list, the latest move would be the product of bilateral conversation.

"It's a big milestone," Mr. Piccone said. "This is the first thing we've seen since the Dec. 17 agreement that says, 'We're jointly agreeing to this step.'"

The historic step would be a major victory for Mr. Obama, who has supported renewed relations with Cuba since his 2008 presidential campaign and made it a core component of his second-term foreign policy agenda.

Mr. Obama met in April with Cuban President Raú l Castro at the Summit of the Americas.

"It seems to be going pretty well according to the script," said Julia Sweig, a Cuba expert and senior fellow at the Lyndon B. Johnson School of Public Affairs at The University of Texas at Austin.

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