The 52-year-old actor and 54-year-old actress have joined The Son, Zeller's first film since his Oscar-nominated 2020 drama The Father.
The Son is based on Zeller's play of the same name. Zeller and Christopher Hampton adapted the screenplay.
The new film follows Peter (Jackman), a man whose busy life with his partner and baby is disrupted when his ex-wife, Kate (Dern), shows up with their teenage son, Nicholas. Peter tries to be a better father to the troubled Nicholas, but the weight of Nicholas' condition sets the family on a dangerous course.
"The Son is a deeply human story which, I believe, connects us all; I hope audiences will be profoundly moved by this family's journey," Zeller said. "Both Hugh and Laura naturally convey great warmth, compassion, and vulnerability ... inviting our audience to embrace and feel every moment."
"The story is set in a vibrant and very much alive New York, an important character. The movie should make us call family and friends to tell them that they are wholly loved and not alone," he added.
Iain Canning, Emile Sherman and Joanna Laurie will produce the film.
Jackman will also star in the new sci-fi thriller Reminiscence, which opens in theaters and premieres on HBO Max in September. Dern will reprise her role as Dr. Ellie Sattler in Jurassic World: Domination, which completed principal photography in November.