The play centers on bullied 15-year-old Anna, whose unexpected friendship with her estranged uncle Terry sends her parents' rocky marriage into a tailspin.
The design team will include Beowulf Boritt (sets), Susan Hilferty (costumes), Natasha Katz (lights) and Obadiah Eaves (original music & sound).
Gomez, who will play Fiona, appeared in The Taming of the Shrew with the Royal Shakespeare Company and the West End production of Boeing, Boeing. Film credits include The Wedding Video, Chromophobia, Subterrain, and The Acid House.
Gyllenhaal, who will play Terry, made his stage debut starring in Kenneth Lonergan's revival of This is Our Youth in London, winning an Evening Standard Theater Award for "Outstanding Newcomer." He received an Oscar nomination for his work in Brokeback Mountain, and is also known for his performances in films such as Donnie Darko and Love and Other Drugs.
O'Byrne, who will play George, won a Tony Award for his work in Frozen and was Tony-nominated for The Coast of Utopia, Doubt, The Lonesome West, and The Beauty Queen of Leenane. He was nominated for an Emmy this past year for his work in HBO's Mildred Pierce . Additional film and television credits include Prime Suspect, Brotherhood, FlashForward, The International, and Brooklyn's Finest.
One additional cast member will be announced shortly.