World leaders have welcomed a deal between the US and Cuba to end more than 50 years of hostility and move towards restoring diplomatic relations.
Leaders in Latin America and Europe praised the courage of US President Barack Obama and his Cuban counterpart.
Pope Francis, who played a central role in bringing the rivals together, also congratulated both men.
They have agreed a number of measures to improve ties, including the release of prisoners on both sides.
Announcing the move, President Obama said the "rigid and outdated policy" of isolating Cuba had clearly failed and that it was time for a new approach.
Leading the praise, Pope Francis sent "warm congratulations" to Obama and Cuban President 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 European Union, which is in the process of normalising 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".
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".
"And the other nations of the Americas should join us in this effort," she added.
The Canadian Prime Minister, Stephen Harper, whose country never broke off ties with Cuba, also welcomed what he called the "overdue development".
But the move was not applauded elsewhere, with some exiled Cubans in Florida reacting with anger and dismay and some Republicans in the US criticising the decision.
"It is a betrayal. The talks are only going to benefit Cuba," Carlos Munoz Fontanil said at a protest in Miami's Calle Ocho.
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 Obama said the US was looking to open an embassy in Havana in the coming months.
Meanwhile, Castro has urged the US to ends its trade embargo, which has been in place since the Cuba revolution led to Communism in the early 1960s.
But power to lift the embargo, which 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.
Officials said that Obama and Castro spoke by telephone on Tuesday for nearly an hour - the first presidential-level talks between the two nations since Cuba's 1959 revolution.
In exchange for 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.
Gross's five-year imprisonment had undermined previous attempts to thaw diplomatic relations between the two countries.
