Writer-director Bruce Robinson started shooting the film March 25.
"The Rum Diary" represents the debut film of Infinitum Nihil, the production company headed by Depp and his sister Christi Dembrowski.
The film is also produced and fully financed by Graham King and his production company GK Films.
Anthony Rhulen and Robert Kravis are also attached to produce. The movie will be shot entirely in Puerto Rico.
Depp befriended Thompson before the eccentric gonzo journalist committed suicide in 2005. The actor portrayed Thompson in the film adaptation of Thompson's book, "Fear and Loathing in Las Vegas."