Depp is the star of the films, Pirates of the Caribbean, Public Enemies and Edward Scissor Hands. In an interview he stated that his great grandmother has a lot of Cherokee heritage. (3)
From an interview in 2002 he stated that he was a mixture of German, Irish and Cherokee among other things.(2) There are some rumors on the internet that Depp also has Lebanese heritage, though this is not confirmed.
Some of Depps biographies state that his family name Depp is of French origin, derived from the names Pierre Deppe or Dieppe. He jokingly says that his surname means idiot in German.
The link below (1) shows a family tree on Depps fathers side that leads right up to his grandfather Oren Laramore Depp. If you go back 9 generations on this family tree it will lead to a woman named Martha, born in 1612, who was a woman of African descent.
An interesting piece of trivia is that Marthas daughter, Elizabeth Key was the first woman of African ancestry to successfully take legal action to free herself from slavery. This happened in 1656. (4)