The meeting is scheduled to take place on the sidelines of the annual gathering of world leaders at the United Nations. Castro is attending for the first time.
The encounter comes as the Cold War adversaries go about the long and complex process of normalising relations following decades of animosity. The US recently eased rules for citizens who want to visit or do business in Cuba, a step aimed at fostering greater economic freedom on the island.
Since then, the two countries have reopened embassies in each other's capitals. But sharp differences remain, particularly over Cuba's human rights record and detainment of political prisoners. Both sides want Congress to lift a longstanding economic embargo against the communist island nation, but many Republican lawmakers and some Democrats want to keep it in place.
Cuba also seeks the return of land occupied by the US Navy base at Guantanamo Bay; the US says that is not in the plan.
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In his address yesterday at the opening of the UN General Assembly's annual ministerial meeting, Obama discussed the shift in policy toward Cuba and said he was confident that Congress "will inevitably lift an embargo that should not be in place anymore."
Obama and Castro first spoke in December after the secret process to restore diplomatic relations was revealed.
They met in person in April while attending a regional summit in Panama. Before then, the last time a US and Cuban leader had convened a substantive meeting was in 1958.
Obama and Castro spoke by telephone again earlier this month before Pope Francis visited Cuba and the United States.
Francis was a go-between for the US and Cuba during their secret talks.