Gyllenhaal is also among the producers.
In the film, Colman will portray a college professor and Johnson a young mum.
"When I finished reading Elena Ferrante's 'The Lost Daughter', I felt that something secret and true had been said out loud," Gyllenhaal explains, "and I was both disturbed and comforted by that."
"I immediately thought how much more intense the experience would be in a movie theatre, with other people around. And I set to work on this adaptation. I find that the script has attracted other people interested in exploring these secret truths about motherhood, sexuality, femininity, desire. And I'm thrilled to continue my collaboration with such brave and exciting actors and filmmakers."