The move comes amid a normalization of ties between the US and Cuba.
Cuba’s presence on the list alongside Syria, Iran and Sudan was a sticking point for Cuba during talks to reopen embassies.
A US trade embargo against Cuba remains and can only be ended by Congress.
Barack Obama met Cuban President Raul Castro at the Summit of the Americas in Panama last week, four months after he announced a historic thaw in ties with the communist island nation.
He said on April 14 that the government of Cuba had “not provided any support for international terrorism” over the past six months.
Barack Obama added that it had “provided assurances that it will not support acts of international terrorism in the future”.
A statement from Josefina Vidal, Cuba’s top diplomat responsible for dealing with the US, said: “The Cuban government recognized the fair decision made by the president of the United States to eliminate Cuba from a list that it never should have been included on, especially considering our country has been the victim of hundreds of acts of terrorism that have cost 3,478 lives and maimed 2,099 citizens.”
In Havana, ordinary Cubans welcomed the move.
Cuba was first placed on the state department list in 1982, for what the US called efforts “to promote armed revolution by organizations that used terrorism”.
The US believes Cuba had long provided a safe haven for members of the Basque separatist group ETA and Colombia’s FARC guerrilla group, according to its 2013 Report on Terrorism.
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.
Republican Senator Marco Rubio, a candidate for the US presidency, condemned the White House decision, saying Cuba remained a state sponsor of terrorism.
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