Depp an haife shi ne a Owensboro, Kentucky, ƙarami daga cikin 'ya'ya huɗu na Betty Sue Palmer (née Wells), mai ba da sabis, da John Christopher Depp, injiniyan injiniya. Depp ya motsa sau da yawa a lokacin yaro. Shi da 'yan uwansa sun zauna a wurare daban-daban fiye da 20, daga bisani suka zauna a Miramar, Florida a shekarar 1970. Iyayen Depp sun saki a 1978 lokacin da yake 15. Mahaifiyarsa ta auri Robert Palmer, wanda Depp ya kira "wani wahayi". Tare da kyautar guitar daga mahaifiyarsa lokacin da yake 12, Depp ya fara wasa a kungiyoyin garage. Shekara guda bayan da iyayensa suka saki, ya fita daga Miramar High School don zama mawaƙa na dutsen dutse. Ya yi ƙoƙari ya koma makaranta makonni biyu daga baya, amma shugaban ya gaya masa ya bi mafarkinsa na zama mawaƙa. Ya taka leda tare da rukuni, wanda ya ji dadin samfurin.
15 na shekara