The Canadian-born moviemaker passed away on Thursday following a brief illness, according to the Montreal Gazette.
Eberts worked on a number of critically acclaimed films during his lengthy career, including Chariots of Fire, Gandhi, Driving Miss Daisy and Dances with Wolves - which all won coveted Best Picture Academy Awards.
He founded independent production company Goldcrest Films, as well as Allied Filmmakers, and also served as chairman of National Geographic Films. In 1992, he was recognised for his achievements with the Officer of the Order of Canada honour.
Director Denys Arcand has paid tribute to his friend, stating, "He was an extraordinary film producer and an extraordinary man. He took filmmaking seriously. He felt cinema should be used to better mankind. This is a lofty standard in an age where movies are being adapted from comic books. He had such noble ideals and morals."
Eberts' most recent project, documentary Jerusalem, is set for release next year.
He is survived by his wife, Fiona, two sons and a daughter.