Depp has two children with Paradis: daughter Lily-Rose Melody Depp (born 1999), and son John "Jack" Christopher Depp III (born 2002).
Bil je tudi član glasbene skupine P, ki je vključevala tudi pevca glasbene skupine Butthole Surfers, Gibby Haynes in basista glasbene skupine Red Hot Chili Peppers, Flea.