The Monty Python comedy troupe will be adding their voices to Chapman's taped recording of A Liar's Autobiography: Volume VI.
Jones told The New York Times that the biopic will be different from traditional films in the genre.
He said that there is "nothing" true about it and that "it's all a downright, absolute, blackguardly lie".
The film will have 15 segments, animated in different styles to resemble the Python aesthetic. It is based on an unreleased home recording of the memoir made shortly before Chapman's death.
Chapman, who met Cleese at Cambridge University, was openly gay but "secretly alcoholic", according to the producers of the film.
Gilliam is to take on the voice of Chapman's mother, while Palin will be playing the father in the 3D film.
The biopic is produced by Jones's son Bill, though fellow producer Jeff Simpson has made clear that it focuses purely on Chapman's life, rather than Monty Python as a whole.
Jones said in a statement: "I had no idea until recently that Graham Chapman is in fact dead - I thought he was just being lazy. However, I am now delighted to find myself working with him again on this exciting project."
BBC 4 commissioned a comedy last week that focuses on the controversy created by the Pythons' Life of Brian film.
Watch the Life of Brian trailer below: