The British moviemaker passed away on 11 March (13), according to The Hollywood Reporter, but the 65 year old's cause of death was unknown as Wenn went to press.
Throughout his career, Hampton worked with the biggest names in the industry, including directors James Cameron, Francis Ford Coppola, George Lucas and Martin Scorsese.
As managing director at Twentieth Century Fox Productions, he was behind the making of Chariots of Fire, The Empire Strikes Back, Omen: Final Conflict and Quest for Fire, and also served as a producer on Sir Ridley Scott's Legend, starring Tom Cruise, as well as on Monty Python's Life of Brian.
Polanski, who worked with Hampton on his 1988 thriller Frantic, called news of Hampton's death "desperately sad", adding, "Tim's warm personality, humour and just outstanding professionalism made him a joy to work alongside... we'll all miss him."
Monty Python funnyman Jones called Hampton "so fresh in my mind, so lively, and so concerned, and so capable," while Palin says, "I have very fond memories of Tim. He kept a remarkably cool head amongst all the madness and he was damn good at his job too... all the Pythons liked and respected him."
Hampton's last production was the 1998 big screen adaptation of Lost in Space, starring William Hurt, Gary Oldman and Heather Graham.
He is survived by his wife Anna, sons Matthew, Piers and Tom from his first marriage to Sally, and grandson William.