He was 59.
Born to English working-class parents, Gibson was accepted into Cambridge University, where he studied pre-med before deciding to pursue a career in film, Daily Variety reported Monday.
In the late 1960s, he began working for the BBC directing scientific documentaries. By the end of the '70s, he had produced some of the BBC's most acclaimed films.
Among his films were "The Juror" (1996), starring Demi Moore and Alec Baldwin; and "What's Love Got to Do with It?" (1993), a critical and box office success chronicling pop star Tina Turner's rise to fame.
Gibson was equally successful in adapting the life story of the music legend Josephine Baker in a film for HBO, "The Josephine Baker Story" (1991), winning the Emmy in direction for Gibson, a Golden Globe for actor Louis Gossett Jr. and a Directors Guild of America nomination for dramatic special.
He is survived by his wife, photographer-singer Paula Guarderas Gibson, two daughters, his mother and a sister. Memorials will be held in London and Los Angeles.