Woods, who is the executor of his late 49-year-old brother Michael's estate, sued Kent Hospital for negligence.
E! News said the hospital's chief executive officer Sandra Coletta told reporters Tuesday mistakes were made in treating Michael.
Coletta also said an institute would be created in the dead man's name and $1.25 million would be put toward research into methods intended to reduce hospital error and improve patient care.
No other details regarding the settlement were disclosed, E! said.
James Woods, 62, has appeared in dozens of films and recently starred in the TV series "Shark."