Filming is taking place at Stone Street Studios, Wellington, and on location around New Zealand.
Production on the films, starring Martin Freeman as Bilbo Baggins, is expected to take up to two years. The first is due out in late 2012.
In January, director Peter Jackson had surgery for a perforated ulcer.
Studios Warner Bros and New Line had previously considered taking the production away from New Zealand after acting unions threatened to boycott the films in protest over payments.
The films had earlier been stalled by problems including rows over distribution rights and the exit of original director Guillermo del Toro.
At a press conference last month, the film’s star, Freeman, joked about the trials it has faced.
“There are some bits of bad luck associated with it,” he said.
“We’re all very optimistic about it. We’re ready to go – just as soon as 2015 comes around.”
The films, which also star Sir Ian McKellen as Gandalf the Grey, Andy Serkis as Gollum, Elijah Wood as Frodo and Cate Blanchett as Galadriel, are based on JRR Tolkien’s epic fantasy novel.
Full story: BBC News – Hobbit filming finally under way