Johnson's wife, Constance, told the network that the 89-year-old TV star died early Thursday morning of kidney failure.
"He died at home, peaceful, in his sleep at 5:21 a.m. today," she said. "[He was] a very brave guy who knew what he wanted, and he wanted to be at home."
Before pursuing a career in acting, Johnson served in World War II. He acted in several TV shows in the 1950s and 1960s, including "The Adventures of Superman," "Alfred Hitchcock Presents" and "The Twilight Zone."
His most famous role came along in 1964 as the beloved Professor on "Gillian's Island."
After the show ended, Johnson appeared in several movies and TV shows, including an episode of "Newhart," where he was shown watching an episode of "Gilligan's Island."
Johnson, a Washington resident, is survived by his wife and daughter, Kim.
ABC News contributed to this report.