The move comes amid a normalisation of ties 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.
A US trade embargo against Cuba remains and can only be ended by Congress.
Mr 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.
The US president said on Tuesday that the government of Cuba had "not provided any support for international terrorism" over the past six months.
He 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 recognised 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."
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