WASHINGTON — President Obama on Wednesday ordered the restoration of full diplomatic relations with Cuba and the opening of an embassy in Havana for the first time in more than a half-century as he vowed to “cut loose the shackles of the past” and sweep aside one of the last vestiges of the Cold War.

The surprise announcement came at the end of 18 months of secret talks that produced a prisoner swap negotiated with the help of Pope Francis and concluded by a telephone call between Mr. Obama and President Raúl Castro. The historic deal broke an enduring stalemate between two countries divided by just 90 miles of water but oceans of mistrust and hostility dating from the days of Theodore Roosevelt’s charge up San Juan Hill and the nuclear brinkmanship of the Cuban missile crisis.

“We will end an outdated approach that for decades has failed to advance our interests, and instead we will begin to normalize relations between our two countries,” Mr. Obama said in a nationally televised statement from the White House. The deal, he added, will “begin a new chapter among the nations of the Americas” and move beyond a “rigid policy that is rooted in events that took place before most of us were born.”

President Obama Announces Beginning of Normalization with Cuba.

In doing so, Mr. Obama ventured into diplomatic territory where the last 10 presidents refused to go, and Republicans, along with a senior Democrat, quickly characterized the rapprochement with the Castro family as appeasement of the hemisphere’s leading dictatorship. Republican lawmakers who will take control of the Senate as well as the House next month made clear they would resist lifting the 54-year-old trade embargo.

“This entire policy shift announced today is based on an illusion, on a lie, the lie and the illusion that more commerce and access to money and goods will translate to political freedom for the Cuban people,” said Senator Marco Rubio, a Republican from Florida and son of Cuban immigrants. “All this is going to do is give the Castro regime, which controls every aspect of Cuban life, the opportunity to manipulate these changes to perpetuate itself in power.”

For good or ill, the move represented a dramatic turning point in relations with an island that for generations has captivated and vexed its giant northern neighbor. From the 18th century, when successive presidents coveted it, Cuba loomed large in the American imagination long before Fidel Castro stormed from the mountains and seized power in 1959.

Mr. Castro’s alliance with the Soviet Union made Cuba a geopolitical flash point in a global struggle of ideology and power. President Dwight D. Eisenhower imposed the first trade embargo in 1960 and broke off diplomatic relations in January 1961, just weeks before leaving office and seven months before Mr. Obama was born. Under President John F. Kennedy, the failed Bay of Pigs operation aimed at toppling Mr. Castro in April 1961 and the 13-day showdown over Soviet missiles installed in Cuba the following year cemented its status as a ground zero in the Cold War.

But the relationship remained frozen in time long after the fall of the Berlin Wall and the collapse of the Soviet Union, a thorn in the side of multiple presidents who waited for Mr. Castro’s demise and experienced false hope when he passed power to his brother, Raúl. Even as the United States built relations with Communist nations like China and Vietnam, Cuba remained one of just a few nations, along with Iran and North Korea, that had no formal ties with Washington.

Mr. Obama has long expressed hope of transforming relations with Cuba and relaxed some travel restrictions in 2011. But further moves remained untenable as long as Cuba held Alan P. Gross, an American government contractor arrested in 2009 and sentenced to 15 years in a Cuban prison for trying to deliver satellite telephone equipment capable of cloaking connections to the Internet.

After winning re-election, Mr. Obama resolved to make Cuba a priority for his second term and authorized secret negotiations led by two aides, Benjamin J. Rhodes and Ricardo Zúñiga, who conducted nine meetings with Cuban counterparts starting in June 2013, most of them in Canada, which has ties with Havana.

Pope Francis encouraged the talks with letters to Mr. Obama and Mr. Castro and had the Vatican host a meeting in October to finalize the terms of the deal. Mr. Obama spoke with Mr. Castro by telephone on Tuesday to seal the agreement in a call that lasted more than 45 minutes, the first direct substantive contact between the leaders of the two countries in more than 50 years.

On Wednesday morning, Mr. Gross walked out of a Cuban prison and boarded an American military plane that flew him to Washington, accompanied by his wife, Judy. While eating a corned beef sandwich on rye bread with mustard during the flight, Mr. Gross received a call from Mr. Obama. “He’s back where he belongs, in America with his family, home for Hanukkah,” Mr. Obama said later.

For its part, the United States sent back three imprisoned Cuban spies who were caught in 1998 and had become a cause célèbre for the Havana government. They were swapped for Rolando Sarraff Trujillo, a Cuban who had worked as an agent for American intelligence and had been in a Cuban prison for nearly 20 years, according to a senior American official. Mr. Gross was not technically part of the swap, officials said, but was released separately on “humanitarian grounds,” a distinction critics found unpersuasive.

The United States will ease restrictions on remittances, travel and banking, while Cuba will allow more Internet access and release 53 Cubans identified as political prisoners by the United States. Although the embargo will remain in place, the president called for an “honest and serious debate about lifting” it, which would require an act of Congress.

Mr. Castro spoke simultaneously on Cuban television, taking to the airwaves with no introduction and announcing that he had spoken by telephone with Mr. Obama on Tuesday.

“We have been able to make headway in the solution of some topics of mutual interest for both nations,” he declared, emphasizing the release of the three Cubans. “President Obama’s decision deserves the respect and acknowledgment of our people.”

Only afterward did Mr. Castro mention the reopening of diplomatic relations. “This in no way means that the heart of the matter has been resolved,” he said. “The economic, commercial and financial blockade, which causes enormous human and economic damages to our country, must cease.” But, he added, “the progress made in our exchanges proves that it is possible to find solutions to many problems.”