The movie, directed by Withnail & I's Bruce Robinson, follows Depp's struggling writer Paul Kemp and his alcohol-fuelled antics working for a run-down newspaper in Puerto Rico. The Kemp character is based on Thompson's own experiences as a 22-year-old.
Depp previously portrayed Thompson in Terry Gilliam's Fear And Loathing In Las Vegas.
Amber Heard, Aaron Eckhart, Giovanni Ribisi and Richard Jenkins co-star in The Rum Diary, opening in the US on October 28 and November 4 in the UK.
Heard recently told Digital Spy of her experiences making Rum Diary: "Johnny Depp is the best at what he does, a dream to work with. I was surrounded by people that really cared about making this movie great, and I hope it will be."