Dornan was cast in the role in August 2019, but had to exit the project due to a production start delay relating to the coronavirus pandemic.
Stephen Frears also recently exited as director of the first two episodes and was replaced by Maggie Kiley.
Written by Patrick Macmanus, "Dr. Death" is based on the terrifying true story of Dallas, Texas neurosurgeon Dr. Christopher Duntsch, who became dubbed Dr. Death after a series of devastating surgeries, which left patients maimed or dead. As victims piled up, two fellow physicians, neurosurgeon Robert Henderson (Baldwin) and vascular surgeon Randall Kirby (Slater), set out to stop him.
Jennifer Morrison and So Yong Kim will also direct episodes of the new show.
Jackson previously had a series regular role on the critically-acclaimed drama series "The Affair", which aired on Showtime. He later starred on miniseries "Little Fires Everywhere" and "When They See Us", the latter of which was directed by Ava DuVernay for Netflix.
The 42-year-old Canadian-born actor is best known for his role as Pacey Witter on the teen drama series "Dawson's Creek" as well as Peter Bishop on the science fiction series "Fringe".