Its last Cuban performance was at the inaugural event in 1960.
While the general travel ban on US tourists remains, it is the latest sign of an easing of relations between the two former Cold War adversaries.
On 3 and 4 November, the company will perform scenes from ballets including Alexei Ratmansky's Seven Sonatas and Fancy Free by Jerome Robbins.
American Ballet executive director Rachel Moore, speaking at a Havana press conference to announce the tour, said: "I can't speak for the politics but I do believe that the arts are a tremendous bridge between communities.
"Dance is an art form that doesn't require a knowledge of language," she added.
The BBC's Michael Voss, in Havana, said the tour almost had to be called off for financial reasons after Washington refused to allow the company's sponsors to support the tour.
Cuban authorities stepped in and agreed to cover the dancers' accommodation and other expenses during the festival, he added.
The company's last appearance at the festival came just a year after Fidel Castro's revolution.
On Tuesday, US officials said the Obama administration was considering loosening travel restrictions to the communist island.
It wants to ease restrictions on travel for US students, researchers and educators as well as for religious and cultural groups.
But there are no plans to ease the 48-year US trade embargo against Cuba.