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Cuban President Raul Castro and Mr Obama met during the Summit of the Americas last week
President Barack Obama will remove Cuba from the US list of state sponsors of terrorism, the White House says.
The move comes amid a normalisation of relations between the US and Cuba.
The Caribbean country’s presence on the list alongside Syria, Iran and Sudan was a sticking point for Cuba during talks to reopen embassies.
Republican Senator Marco Rubio condemned the White House decision, saying Cuba remained a state sponsor of terrorism.
“They harbour fugitives of American justice, including someone who killed a police officer in New Jersey over 30 years ago,” said Mr Rubio, a Cuban American who launched his 2016 presidential campaign on Monday.
“It’s also the country that’s helping North Korea evade weapons sanctions by the United Nations.”
Mr Obama announced the historic US thaw with Cuba in December but the US trade embargo against the country remains, and may only be ended by Congress.
Analysis – Thomas Sparrow, BBC Mundo, Washington
This decision is the most concrete step to date taken by the US government to try and dismantle the structures that prevented a normal relationship between both countries for decades.
And it carries a lot of weight too, because it officially changes the way the US government has viewed Cuba since 1982.
The White House now believes Cuba does not support rebel groups such as Farc or ETA and – more importantly – it thinks the government will not do so in the future.
This is a significant message of confidence by the Obama administration towards the Cuban government.
Mr Obama said the government of Cuba “has not provided any support for international terrorism” over the last six months and had “provided assurances that it will not support acts of international terrorism in the future”.
White House press secretary Josh Earnest said the US still had differences with Cuban policies and actions, but they were not “relevant” to the terror list.
BBC