Andrew Haigh -- whose credits include Looking, 45 Years and The OA -- wrote the screenplay and is directing the project.
Based on the 2016 novel by Ian McGuire, The North Water follows a disgraced ex-army surgeon (played by O'Connell) working as the ship's doctor on a whaling expedition to the Arctic.
The cast and crew recently spent three weeks shooting scenes in the Norwegian archipelago Svalbard. Production is now scheduled to move on to Hungary.
"Filming on the ship was an incredible experience and one that I will never forget. To be so privileged to see such beautiful animals like polar bears in their natural habitat -- albeit it an ever changing one, sadly -- was truly remarkable," Graham said in a press release on Friday.
The series will include three, hour-long episodes and one 90-minute episode.
No premiere date has been set yet.