Pope Francis joined leaders from Latin America and Europe in praising the “historic” deal which saw the release of prisoners from both countries.
However, dozens of dissident Cubans oppose the move, which some Republicans have labeled a “retreat” by the US.
US-Cuban ties have been frozen since the early 1960s.
President Barack Obama said the “rigid and outdated policy” of isolating Cuba since then had clearly failed and that it was time for a new approach.
President Raul Castro, meanwhile, has urged the US to ends its trade embargo, which has been in place since the Cuba turned to Communism more than 50 years ago.
Power to lift the embargo, which Raul Castro says has caused “enormous human and economic damage”, lies with the US Congress, and correspondents say many Republicans are still deeply opposed to this.
Leading the praise, Pope Francis sent “warm congratulations” to Barack Obama and Raul Castro for overcoming “the difficulties which have marked their recent history”.
The announcement followed more than a year of secret talks in Canada and at the Vatican, directly involving the pontiff.
The EU, which is in the process of normalizing ties with Cuba, described the move as a “historical turning point”, while leaders meeting at a Latin America summit in Argentina broke into applause at the news.
Chilean Foreign Minister Heraldo Munoz hailed it as “the beginning of the end of the Cold War in the Americas”.
Venezuela’s President Nicolas Maduro, whose predecessor Hugo Chavez was a close ally of Fidel Castro, said it was a “moral victory” and “victory for Fidel”.
Former US Secretary of State Hillary Clinton said increased US engagement in Cuba in the future should “encourage real and lasting reforms for the Cuban people”.
Canadian PM Stephen Harper, whose country never broke off ties with Cuba, welcomed what he called the “overdue development”.
However, the move was not applauded by everyone, with dozens of Cubans living in exile in the US state of Florida protesting after the announcement on December 17.
Meanwhile, Republican Senator Marco Rubio slammed the deal as “inexplicable”, adding that it did nothing to address the issues of Cuba’s political system and human rights record.
As part of the deal, US contractor Alan Gross, 65, was released from Cuban prison in return for three Cubans held in the US.
President Barack Obama said the US was looking to open an embassy in Havana in the coming months.
Officials said that Barack Obama and Fidel Castro spoke by telephone on December 16 for nearly an hour – the first presidential-level talks between the two nations since Cuba’s 1959 revolution.
In exchange for Alan Gross, who was in poor health, and an unnamed American intelligence officer, Washington released three members of the so-called “Cuban Five” who were serving lengthy sentences for espionage.
Alan Gross’s five-year imprisonment had undermined previous attempts to thaw diplomatic relations between the two countries.
lwo6Ec6DgkkImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…