It's the first New Zealand-backed film for Adamson since returning home after more than a decade in Hollywood as director and producer on the Shrek and Chronicles of Narnia movies.
Adamson, who lived in Papua New Guinea in his teens and speaks pidgin, shot the film last year on Bougainville Island where Jones set his story against the territory's 1991 civil war. Some scenes depicting Victorian London were filmed in Oamaru.
Published in 2006, Jones' book was shortlisted for the 2007 Man Booker Prize, among other accolades.
Laurie was a fan of the book before taking on its central role, Mr Watts, who fills in as island school teacher and whose readings from Dickens' Great Expectations inspire young Matilda.
He says in the film's publicity notes: "When I heard that there was a film in the offing, my ears pricked up because I was absolutely gripped by the story. The news got better when I heard the script had been written by Andrew Adamson - a very clever fellow. He's been brave with it. Brave but respectful, a very hard balance to pull off."
Jones, who wasn't involved in the script adaptation, says he was pleased with the casting. "When I heard that Hugh Laurie was to play Mr Watts, a penny dropped: 'Well, of course. Who else?"'
Matilda is played by Xzannjah Joel, a Bougainville teenager Adamson cast after bringing her to New Zealand for acting workshops. Matilda's mother Dolores is played by Xzannjah's own mother, Healsville Joel, who had to take time off from her work as a doctor at a Bougainville hospital for filming.
Her daughter's performance has already drawn a comparison with in another New Zealand film which had the Toronto festival as a launchpad.
Says her acting coach Rawiri Paratene: "The camera adores her. She is gorgeous and it's not just her face. It's not just the physical beauty that she brings. She's a 14-year-old-girl going on eight and this is a quality that is incredibly appealing to an audience. Innocence. I've worked with this quality before - with Keisha Castle-Hughes in Whale Rider."
Others involved in the film include Tim Finn, who contributed to the soundtrack, and Lord of the Rings production designer Grant Major and costume designer Ngila Dickson.
Mr Pip is unlikely to reach New Zealand screens until next year.
Meanwhile, Auckland-based Adamson also directed the James Cameron-produced 3D film Cirque du Soleil: Worlds Away , a performance by the international circus franchise which is due to open the Tokyo International Film Festival next month.