The filmmaker was admitted to Wellington Hospital in New Zealand after suffering acute stomach pains.
Jackson, 49, has since had surgery for the perforated ulcer and released a statement regarding his progress.
It said: 'Sir Peter is currently resting comfortably and his doctors expect him to make a full recovery.'
The statement added that the start of filming would now be slightly delayed but it is expected he will return to his directing duty soon.
Filming is due to start in February and it was confirmed that he has been scouting out locations in Queenstown.