A band spokesman said the show in the capital Havana on 25 March was "the first open air concert in Cuba by a British rock band".
The Stones are currently on a Latin American tour due to end on 17 March in Mexico City.
The Havana gig will come three days after an historic visit to Cuba by US President Barack Obama.
In a statement, The Rolling Stones said: "We have performed in many special places during our long career, but this show in Havana is going to be a landmark event for us, and, we hope, for all our friends in Cuba too."
Rock music was marginalised in Cuba for political reasons after the Cuban revolution in the 1950s which saw Fidel Castro come to power.
In 2001, Manic Street Preachers became the biggest British rock band to play in the country, putting on a show at Havana's Karl Marx Theatre which was attended by the Cuban president.
The Stones' America Latina Ole tour also includes shows in Brazil, Peru and Colombia.
The Havana gig will be filmed by director Paul Dugdale, who has previously worked with One Direction, Adele and Coldplay.
The Rolling Stones have announced they are to give a free concert in Cuba later this month.