And that rounds off our live coverage of developments. You can stay up to date with the latest on this story here. Thanks for joining us.
Protests against the thawing relations continued in Miami on Tuesday afternoon.Copyright: EPA
BBC News, Washington
tweets: "This isn't just about US-#Cuba relations. Senior US officials say will be trans-formative in US policy in Latin America overall"
BBC business reporter, New York
"It could signal a shift from money flowing into Cuba's state-run sector and into the hands of private citizens."
Read Kim's analysis of what this means for US and Cuban economies.
on how Russian state television is reporting the story.
"This news has become a real sensation. The White House regards its policy in relations with the Island of Freedom as a failure. Decades later, the Americans have acknowledged that the Cuban embargo did not correspond to the USA's interests. Although this policy, as the White House says, was pursued for the best of intentions, as always, however, it had no effect."
Senators Pat Leahy and Jeff Flake, and Congressman Chris Van Hollen flew to Cuba to bring Gross back to the US.Copyright: Getty Images
The BBC's Suzanne Kianpour was at the Alan Gross press conference earlier in Washington DC.
"The family spokesperson had warned the press about his missing teeth before he walked out - and for a man who'd been held captive for five years, there was a certain youthful candour about his concern for his appearance. He urged the press to give him time and privacy to 'get his teeth fixed' before any interviews - punctuating his request with 'claro?' - in a surprisingly authentic Cuban accent."
Jeb Bush, who was Florida governor and is considering running for president, told USA Today: "I don't think we should be negotiating with a repressive regime".Copyright: AP
More details have been emerging about the second person released by Cuba as part of the deal. He was a Cuban male who gave crucial intelligence to the US - and paid the price.
"This man, whose sacrifices were known only to a few, has spent nearly 20 years in a Cuban prison," the US Office of the Director of National Intelligence (ODNI) said in a statement.
There's a profile of this unnamed detainee here.
Liliet Heredero, BBC Mundo, Miami
"This will have a huge impact on Cuba but it will prove controversial and won't be easy to implement."
You can watch Liliet's interview in which she talks about the mood in Miami.
A New York Times editorial describes this as "a bold move that ends one of the most misguided chapters in American foreign policy".
BBC News, Washington
tweets: "Senior admin officials: 'if there's any US foreign policy that's passed it's expiration date, it's US-#Cuba policy'"
Anti-Castro activists in Miami made their feelings heard in protests denouncing the Cuban leader.Copyright: Reuters
Ignacio de los Reyes
BBC Mundo, Buenos Aires
Argentine media highlighted the intermediation of Pope Francis in the dialogue between Cuba and the United States, as noted by Obama himself.
The Pope is trending on social networks such as Twitter in this part of the world. Francis was already a highly rated leader in Argentina. His role in these negotiations secure a further boost in his popularity.
BBC business reporter, New York
tweets: "Spoke w/ cigar seller in FL, he told me he's sending celebratory boxes to both Castro & Obama 'for a job well done'"
Daniel Pardo, BBC Mundo, Caracas
The announcement had great impact in Venezuela, where all news related to Cuba is widely covered. It happened just a week after the US issued sanctions against Venezuelan officials, which were strongly condemned by President Nicolas Maduro.
On Monday, he led a protest against the US but on Wednesday, Maduro celebrated the release of three Cubans detained in the US.
"We have to acknowledge that this is a courageous move from president Obama", he said during a Mercosur meeting he was attending in Buenos Aires.
Earlier, Alan Gross made jokes with reporters about his teeth, but his confinement had clearly taken its toll.Copyright: AFP
Barbara Plett Usher, BBC News
Cuba has stopped exporting revolution to Latin America. In fact, it's mediating the most successful attempt so far to achieve peace between the Colombian government and FARC rebels, making its inclusion on the US list of states that sponsor terrorism look increasingly out-dated.
Latin American countries think so: they've reintegrated Cuba into regional bodies by inviting it to the Summit of the Americas in April. President Obama is also expected to attend, which perhaps helped focus his mind as he ponders how to shape his legacy during his remaining two years in office.
Barbara Plett Usher, BBC News
The release of Alan Gross was essential to any diplomatic breakthrough between the United States and Cuba, but internal political changes in both countries had already created a climate where detente was conceivable.
In the US, demographic shifts in Miami have softened the political influence of the anti-Castro exiles: younger Cuban Americans and recent immigrants are more open to engagement. In Cuba, limited economic reforms carried out by Raul Castro have begun to relax the tight grip of the state, and pique the interest of American business.
ABC's political director Rick Klein tweets about the pro-baseball league's reaction to the news: "MLB is watching... 'will keep our Clubs informed if this different direction may impact the manner in which they conduct business' in Cuba".
US President Barack Obama telephoned Cuban President Raul Castro on Tuesday, speaking for nearly an hour.Copyright: Getty Images
He watched Mr Obama's speech alongside Secretary of State John Kerry and said he was excited by the changes outlined. "It's good to be home," he added, as he finished his short speech.
In no way are the people of Cuba responsible for his "ordeal". It pains me to see them hurt by "mutually belligerent policies", says Mr Gross.
Mr Gross is speaking to reporters just an hour or so after an emotional return to US soil.Copyright: Reuters
"In my last letter to President Obama, I said despite my five years of captivity I said I would not want to trade places with him."
"It was crucial to know I was not forgotten," he adds.
"To all of those who tried to visit me, but could not, thank you for trying," Mr Gross says.
Mr Gross thanks President Obama, his wife and his lawyer for his release.
"This is great" Alan Gross says as he walks into a room full of reporters. "Today is the first day of Hanukkah and this the best Hanukkah I will celebrate in a while."
You can watch his statement live here.
Alan Gross, the key to all the dramatic developments today, is about to speak now.
Gloria Borger, CNN's chief political analyst, has just popped up on air and warns that Obama still needs Congress approval for funds and that's not guaranteed.
BBC NewsCopyright: BBC
BBC business reporter, New York
One big winner in this could be US farming. Under relaxed restrictions put in place under President Bill Clinton but that effectively happened under George W Bush, US agribusinesses were allowed to export to Cuba. From 2000 to 2013, those exports were an estimated $4.7bn (£3bn). Since Cuba imports an estimated 80% of its food, the loosening of restrictions could help those firms - in addition to firms like Cargill which could be able to export agricultural equipment to the country.
Earlier, Havana residents watched history unfold as Cuban President Raul Castro told the nation about a new era.Copyright: Reuters
US Republican Senator Lindsey Graham tweets: "I will do all in my power to block the use of funds to open an embassy in Cuba. Normalising relations with Cuba is bad idea at a bad time."
US President Barack Obama has also instructed Secretary of State John Kerry to review Cuba's designation as a state sponsor of terrorism. The country was placed on the ignominious list in 1982.
#BBCtrending looks at what Cuban twitter users were saying in the wake of the announcement.Copyright: Trendsmap.com
tweets: "US glad to get back Alan Gross. But 'one of the most important intelligence agents that US has ever had in Cuba' surely a bigger prize?"
You can now watch the BBC's video of President Barack Obama addressing the US on Cuban policy changes and vowing to "cut loose the shackles of its past".
Alan Gross is scheduled to speak in Washington DC shortly.Copyright: Reuters
In a statement, Secretary of State John Kerry says the US believes "the risk and the cost of trying to turn the tide is far lower than the risk and cost of remaining stuck in an ideological cement of our own making".
In a statement from the Holy See, Pope Francis says he expresses his "warm congratulations" to the US and Cuba for today's announcement and will "continue to assure its support for initiatives which both nations will undertake to strengthen their bilateral relations and promote the wellbeing of their respective citizens".
Florida Senator Marco Rubio, a Cuban-American, Republican and possible 2016 presidential contender, said the US new policy would do nothing to address human rights issues in Cuba.
"But it potentially goes a long way in providing the economic lift that the Castro regime needs to become permanent fixtures in Cuba for generations to come," Mr Rubio said.Copyright: EPA
Who are the Cuban Five? Four years ago, the BBC looked into the case of five Cubans imprisoned in Florida, three of whom are heading back to Cuba today,
BBC business reporter, New York
Currently, US remittances to Cuba - often sent by Cuban Americans to family members - are estimated to be around $2bn a year. President Obama's action effectively quadruples the amount that US citizens can send to Cuba from $500 to $2,000.
That could be a big boon to the Cuban economy, and in particular, the fledgling private sector. It also solves a problem currently facing the Cuban economy, which needs at least $2.5bn in outside investment to maintain a steady growth rate. With Venezuela suffering as a result of plunging oil prices, this could solve the country's current economic crisis.
A dialogue between Cuba and the US was authorised in spring of 2013, senior administration officials say. Multiple meetings between the two nations took place in Canada as well as the Vatican.
In January the BBC spoke to the first group of Cuban exchange students in Miami in 50 years about life in Cuba versus life in Florida.
Bolstering telecommunications in Cuba is a priority for the Obama administration, with officials saying they will authorise the export of certain communication devices, software, hardware and services to the island nation.
US President Barack Obama told the nation the isolation policy had failed.Copyright: AP
The Daily Beast reports US officials at Guantanamo Bay, a small part of Cuba used as a US naval base, including the prison of al-Qaeda suspects, were taken aback by today's announcement.
The Obama administration's changes in Cuban policy now mean visitors to the island nation can bring up to $100 in Cuban cigars back to the US. But, officials note, the cigars must be for personal use and not re-sale.
New York Times' Binyamin Appelbaum tweets: "The arc of history is long but it bends toward Americans being able to use their credit cards in every country on earth."
Cubans watched their leader, Raul Castro, address the nation on Wednesday following the announcement of US policy changes.
David Botti, BBC News
Among those upset at the prisoner swap is Senator Robert Menendez, a Cuban-American and staunch anti-Castro politicianCopyright: BBC
US President Barack Obama and Cuban President Raul Castro spoke on the phone on Tuesday for nearly an hour, a senior administration official says. They discussed potential for cooperation on a range of issues, including fighting the spread of Ebola and counter-terrorism.
At the meeting between US Secretary of State John Kerry and Alan Gross and his family, Mr Kerry expressed his "overwhelming happiness" Mr Gross is now free, a State Department spokeswoman says.
CNN's national security correspondent Jim Sciutto tweets :"@JohnKerry embraces #AlanGross as he lands at Andrews AFB on his return home from #Cuba"Copyright: CNN
Differences remain between Cuba and the US in areas such as human rights and foreign policy, President Castro added.
"We have agreed to re-establish diplomatic ties after more than half a century," he said in a nationally broadcast address. But the US trade embargo, which he called the "blockade", remained unresolved, he added.
Cuban President Raul Castro was also speaking in a TV address at the same time as Mr Obama. He confirmed Cuba had agreed to re-establish diplomatic ties with its Cold War enemy.
There is a large gap in how younger and older Cuban Americans feel about the US relationship with Cuba.Copyright: BBC
"Change is hard, in our own lives and the lives of nations," Mr Obama says as he closes his address. "Today we are making these changes because it is the right thing to do."
Mr Obama thanks Pope Francis, the government of Canada and a bipartisan group of members of Congress for their assistance in advancing changes in US-Cuban policy.
We should not allow US sanctions to add to the burden of Cuban citizens we seek to help, Mr Obama says in his televised speech.
"I do not expect the changes I am announcing today to bring about a transformation of Cuban society overnight," Mr Obama explains.
Cuban journalist Elaine Diaz tweets: "Listening Obama, praying"Copyright: BBC
The US will open an embassy in Havana in the coming months, Mr Obama says.
"I look forward to engaging Congress in an honest and serious debate" about lifting further restrictions codified in US law, Mr Obama adds.
"Increased commerce is good for Americans and Cubans," Mr Obama says of restrictions lifted on trade and commerce between the two nations.
"Isolation has not worked. It's time for a new approach," Mr Obama says of the embargo policy against Cuba in place since 1961.
Mirta Ojito, Cuban American journalist, tweets: "Raul Castro still unhappy that 'blockade' remains in place."
Also released was an unnamed agent who had gathered crucial intelligence for the US government, he says.
He was released by the Cuban government on humanitarian grounds, says the president.
The wrongful imprisonment of US citizen Alan Gross for five years in Cuba was a major impediment to policy changes, Mr Obama claims.
David Botti, BBC News
Many of the Cubans who left the country have moved to nearby Florida, especially in Miami - the state's southern most city and only 90 miles (144km) away from Cuba.Copyright: BBC
Neither the American or Cuban people are well served by a "rigid" policy imposed decades earlier, Mr Obama adds.
Sanctions have had little effect, says Mr Obama.
US President Barack Obama is making a TV address now.
US Republican Senator Marco Rubio has spoken out against easing ties with Cuba. His family fled the country and he's been tipped for a presidential run in 2016.
"Today's announcement initiating a dramatic change in US policy toward Cuba is just the latest in a long line of failed attempts by President Obama to appease rogue regimes at all costs."
Two members of the Cuban Five were earlier released, one in 2011 and another in February. Fernando Gonzalez (below) received a hero's welcome.
Cuba has maintained they posed no threat to the US and were only monitoring anti-communist exiles in Florida with the aim of preventing attacks by exiles on Cuba.
The three Cubans released from the US on Wednesday were members of the Cuban Five, found guilty of conspiracy and failure to register as foreign agents in the US in 2001.
The unnamed US asset was responsible for important intelligence gathering which led to prosecution of multiple individuals. "His return was particularly important to us," the administration official told reporters.
Three Cubans imprisoned in the US have been exchanged for one unnamed intelligence asset held in Cuba for 20 years, a senior US administration official says.
Jeff Flake, a US congressman from Arizona, tweeted this picture of Alan Gross on US soil.Copyright: Jeff Flake
American aid worker Alan Gross has arrived at Andrews Air Force Base near Washington from Cuba, according to pictures broadcast on US TV.
He was released by Cuba as part of a deal that also saw the release of three Cubans jailed for spying by the US.
US President Barack Obama and his Cuban counterpart Raul Castro are expected to make simultaneous statements at 17:00 GMT.
American officials have told US media that Washington is looking to open an embassy in Havana in the coming months.
Welcome to our rolling coverage of the historic announcement that the US and Cuba are to begin working towards normalising diplomatic relations.
The announcement marks a huge shift in ties between the two countries, which have been strained for more than 50 years, since the Cold War era.