According to The Hollywood Reporter, Shrek 2 writer Andrew Adamson is writing and directing the film.
Lloyd Jones wrote the novel, which centres on a man who opens a school in war-torn Bougainville, Papua New Guinea and reads Great Expectations to his students.
"From the first words of the novel, and the first image of the screenplay, I was hooked on Mr Pip," said House star Laurie, who recently played a blues show at a small bar in New Orleans.
The actor continued: "It's an immensely touching, unique, yet completely unsentimental story of love. It is unlike any script I have read, or any story I have ever heard. Plus I get to go to Papua New Guinea and call it work. I am a very lucky man."
"I read Mr Pip on a transatlantic flight and, by the time of landing, knew I would make this film," Adamson said.
He added: "It's a testament to Lloyd's wonderful novel that it has captured the hearts of Hugh, [producers] Robin [Scholes], Leslie [Urdang] and an incredible group of like minded collaborators."
Laurie signed a deal earlier this year to record a blues album.