The world premiere of the drama is scheduled to take place next spring.
The production marks Allen's first return to Broadway since "The Heidi Chronicles" in 1989 and Irons' first time back on Broadway since "The Real Thing" in 1984. Irons won a Tony Award for his work in that play.
"Impressionism" is the story of "a world traveling photojournalist and a New York gallery owner who discover each other and also that there might be an art to repairing broken lives," said a release issued by the show's representatives.
Irons has appeared in the films "Reversal of Fortune,"The French Lieutenant's Woman," "Die Hard with a Vengeance," "Lolita," "The Man in the Iron Mask" and "Merchant of Venice." Irons also provided the voice for the character Scar in the animated film "The Lion King."
Allen won a Tony Award for her Broadway debut in Lanford Wilson's "Burn This" in 1988.
She has appeared in the films "The Contender," "The Crucible," "Nixon," "Pleasantville" and "The Upside of Anger."