Based on Hunter S Thompson's novel of the same name, the movie stars Depp as American journalist Paul Kemp working in Puerto Rico.
The first poster features a half-naked Depp opening the curtains of his room to see an aeroplane with a sky banner reading "Welcome to Puerto Rico".
The second image features a close-up of Depp's face and, like the first, boasts the tagline "Absolutely nothing in moderation".
Thompson's book was originally written in 1959, but was not published until 1998. The film adaptation is being directed by Withnail & I helmer Bruce Robinson, whose last film was Jennifer 8 in 1992.
Depp has said that he promised Thompson that he would get the movie made. The writer died in 2005.
Co-star Amber Heard has said that she hopes the film "gets all the attention and accolades it deserves".
> Johnny Depp's 'The Rum Diary' teaser poster released
Watch Johnny Depp in The Rum Diary trailer below: