WASHINGTON – The United States will restore diplomatic relations with Cuba in the most sweeping changes to U.S.-Cuba policy since President Dwight Eisenhower severed ties with its communist rulers and the two countries faced each other in the most dangerous flash point of the Cold War.

President Obama said Wednesday that he's scrapping an "outdated approach" to opening the island to democracy after reaching a deal with Cuban leader Raúl Castro to release an American jailed in Cuba and three Cubans convicted of spying on the U.S.

"These 50 years have shown that isolation has not worked," Obama said at the White House, announcing the changes as Alan Gross, imprisoned on the island for five years, arrived in the U.S. "It's time for a new approach."

The deal — reached after months of secret negotiations in Canada and at the Vatican — also involved the release from prison of a Cuban man Obama described as "one of the most important intelligence agents" that the United States ever had in Cuba.

As a result, the United States will set up an embassy in Havana and possibly remove Cuba from the list of states that sponsor terrorism.

The thaw comes decades after the U.S. drew a bright line in response to the revolution on the island 90 miles from Florida, ordering an embargo in 1960 after the government nationalized all American-owned property, cutting off official contact with the Cuban government in January 1961, backing a failed invasion later that same year, and then going to the brink of nuclear war with the Soviet Union over missiles in Cuba in 1962.

Now, in addition to opening an embassy, the U.S. will loosen restrictions on travel and trade with the country, making it easier for more Americans to travel there and allowing them to bring back as much as $400, including $100 worth of alcohol and tobacco.

It will permit the export of certain goods, including building materials for private housing and goods for use by private-sector Cuban entrepreneurs, and allow U.S. credit and debit cards to be used by travelers to Cuba.

The moves are a nearly complete repudiation of the economic stranglehold the U.S. sought to impose soon after Fidel Castro came to power in 1959. Obama said the effort to secure openness and democracy on the island by tightening economic screws has "failed to advance our interests."

Helping the Cuban people

"I do not expect the changes I am announcing today to bring about a transformation of Cuban society overnight," Obama said. "But I am convinced that through a policy of engagement, we can more effectively stand up for our values and help the Cuban people help themselves as they move into the 21st century."

The moves stop short of lifting the decades-old economic embargo against Cuba, which only Congress can do. But Obama said he would look forward to an "honest and serious debate" about the possibility.

That could prove difficult. The changes drew backing from the U.S. Chamber of Commerce and agricultural interests that have long eyed Cuba as a lucrative market, but were met with sharp opposition from some of the staunchest anti-Castro lawmakers in Congress. They said the loosening of the restrictions will only enrich the Castro regime and embolden its efforts to crack down on its critics.

Sen. Marco Rubio, R-Fla., the Cuban-American incoming chair of a Senate Foreign Relations subcommittee, pledged to try to block what he called a "dangerous and desperate attempt by the president to burnish his legacy at the Cuban people's expense."

Obama said he spoke Tuesday with Raúl Castro to review the deal and "made clear my strong belief that Cuban society is constrained by restrictions on its citizens."

Tensions still remain

Gross was flown to Andrews Air Force Base outside Washington aboard one of the jets used for the president and other high-ranking government officials. "It was crucial to my survival knowing that I was not forgotten," he said.

White House officials said the loosening of restrictions was not in response to a Cuban request but are in the U.S. national interest.

Cuba wanted the U.S. to end its democracy programs — like the one Gross was engaged in — and return use of the Guantanamo Bay Naval Station, but the U.S. refused, said an administration official. "We'll continue to have strong differences," the official said.

The high-level talks — nine in all — began in June 2013 but were given considerable "confidence and momentum" by Pope Francis, White House officials said. The pope, after talking about Cuba with Obama at a Vatican meeting last March, wrote letters to Obama and Castro, calling on them to resolve the issues of the prisoners "in order to initiate a new phase in relations between the two parties."

Obama has no trip to Cuba planned but is open to the idea.

"I don't have any current plans, but let's see how things evolve," he told ABC's David Muir. No American president has visited Cuba since Calvin Coolidge in 1928.