The match comes after Washington and Havana announced Dec. 17 that they would negotiate the restoration of diplomatic relations that were severed shortly after the 1959 Cuban Revolution.
"The shift of last Dec. 17 is a great step, very beneficial for our soccer," said Cuban Soccer Association vice-president Antonio Garces.
He said the Cosmos are expected to play in Havana on June 2. It's the first such visit by a club team since the now-defunct Chicago Sting came here in 1978, though the U.S. national team played a World Cup qualifier in Havana in 2008.
Cosmos officials are expected to visit beforehand to discuss the match.
"The United States plays excellent soccer, so for us it will be great preparation for the knock-out phase of 2018 World Cup" qualification, Garces said.
Cuba is to play a series on June 8 and 16 against the winner of a series between Curacao and Montserrat.
The Cosmos compete in the second-tier North American Soccer League. The team's roster includes Raul Gonzalez, a longtime star with Spain's national team and club powerhouse Real Madrid.
Sports exchanges between Cuba and the United States increased in recent years, including several visits by U.S. college baseball players.
Baseball is the most popular sport in Cuba, but soccer has made strides in recent years with many young people sporting jerseys of Real Madrid and Barcelona.