Dozens of Cubans risk their lives daily, illegally crossing several countries to get to the US.
The US and Cuba have agreed on a historic deal to re-establish full diplomatic relations, severed 54 years ago in the heat of the Cold War.
Presidents Barack Obama and Raul Castro exchanged letters on Wednesday agreeing to unfreeze ties on July 20, when embassies in Washington and Havana can be reopened.
Obama – who was born the year the US embassy was closed, in 1961 – hailed the deal as a “historic step forward” that would end a failed and archaic US policy of isolating the island.
Secretary of State John Kerry, speaking from Vienna, said he would visit Havana to raise the US flag outside the future US embassy.
On July 20, Castro will send Foreign Minister Bruno Rodriguez to open the Cuban embassy in Washington.
The delegation will include “prominent representatives of Cuban society”, the government said in a statement.
Both countries are currently represented by an “interests section” within the embassies of Switzerland.
“The progress that we mark today is yet another demonstration that we don’t have to be imprisoned by the past,” Obama said from the White House Rose Garden. “When something isn’t working, we can – and will – change.”
Isolating Cuba had been a foreign policy pillar under 10 US presidents, continuing long after the fall of the Soviet Union in 1991. Washington’s allies repeatedly condemned the policy, and Obama declared it had failed to promote democracy or improve the lives of Cubans living in a one-party state.
“It hasn’t worked for 50 years. It shuts America out of Cuba’s future, and it only makes life worse for the Cuban people,” Obama said while noting stark differences between the two governments would remain.
In the largest Cuban enclave in the US, in Miami, the thaw in relations has been met with mixed reactions.
Al Jazeera’s Andy Gallacher, reporting from the community known as Little Havana, said many in the younger generation welcome the move but some older Cuban immigrants see Obama talking to Cuba as “nothing less than treason”.
One woman said: “I don’t know what Obama is thinking. The Cuban people is going to benefit? The Cuban people is going to get nada [nothing].”
The move to normalise relations still faces stiff opposition from Republicans in the US Congress.
Senator Marco Rubio, a Cuban-American presidential candidate, is already threatening to block the nomination of an ambassador to the island.