His secretary of 53 years, Evelyn Christel, said he died at Stony Brook University Medical Center on Long Island of natural causes a day after his 88th birthday, according to The Associated Press.
Robertson remained a popular actor from the mid-1950s into the following century. His later roles included Uncle Ben in Sam Raimi's "Spider-Man" movies.
"My father was a loving father, devoted friend, dedicated professional and honorable man," daughter Stephanie Saunders said in a statement. "He stood by his family, friends, and colleagues through good times and bad. He made a difference in all our lives and made our world a better place. We will all miss him terribly."
He won the Academy Award in 1968 for his performance in Charly playing a mentally disabled man who undergoes medical treatment that makes him a genius until he regresses to his former state.
Robertson's funeral is set for Friday in East Hampton. You can read more about his life and career by visiting this link.
(Photo Credit: WENN.com)