Crowds had waited hours to greet the star, who spent some time meeting and greeting old and young fans.
Co-star Amber Heard turned on the glam with a stunning white figure hugging dress.
The beautiful French star Eva Green, most famous for her role in Casino Royale, attended the premiere.
The film is a project Depp was keen to get off the ground for many years, being a keen fan and friend of author Hunter S. Thompson since starring in Fear and Loathing in Las Vegas in 1998. He petitioned retired director Bruce Robinson, of cult favourite Withnail and I fame, to direct the film. The story is a semi-autobiographical account of an American writer who goes to work for a run-down newspaper in Costa Rica.
See the trailer for The Rum Diary.