Directed by Darren Aronofsky, the movie is about the rivalry between two dancers at a competitive ballet company in New York.
"The cast and crew of 'Black Swan' are both excited and humbled by the selection committee's invitation," the BBC quoted Aronofsky as saying in a statement. "It is an honor to walk the great red carpet on the Lido, and we are excited to premiere our film to the wonderful audiences in Venice."
The festival is to run from Sept. 1-11.
Celebrity Families of 2014 [PHOTOS]