You could break this up into two parts - When did the famous GAOP pirates start using skulls and skeletons in their iconography? When did the media start associating these pirates with voodoo and when did they start featuring pirate decor with a lot of skeleton motifs?

First, the iconography. Simple answer - the early eighteenth century. The early eighteenth century marked a significant change for piracy since pirates changed for the British. It changed from being raiders who were still loyal to their home country (and even flew their colors) and expected to be welcomed home where they could reunite with loved ones (while they tipped a bribe to local authorities), to sea thieves who would not be tolerated by the colonies (especially their governments) anymore. The heavily British pirates in the Atlantic increased their attacks on British ships dramatically and finally became the "enemies of mankind" since more and more of them no longer respected the authority of any of the recognized European powers. The pirates began adapting familiar death iconography of the period and put it on their flags. E.T. Fox covers this in tons of detail in his book Jolly Rogers, the True History of Pirate Flags. So that's where the skull/skeleton iconography began, but it's only seen on their flags and nothing else. If you want more detail, I highly recommend buying the book.

Second, Hollywood. In regards to mainstream American media portrayal, there are three culprits as far as I can find. Disney, Tim Powers, and Ron Gilbert. In imagery of historical pirates in the nineteenth and first half of the twentieth century, you occasionally see artists and other creators of media place the skull and crossbones in various places on pirate clothing and other things pirate used in these depictions - but it wasn't on a huge scale. One example that sticks in my head is in the 1920s silent film The Black Pirate, the boats that the pirates arrive in alongside the big ship have skull and crossed bones painted on the bow, as if to make sure the audience got "that's a pirate boat" or something to that effect. But the significant point comes in the 1960s, when Disney developed an attraction for Disney Land called "Pirates of the Caribbean." This ride starts with not only a Louisiana Bayou, but a cave full of skeletons draped on and around treasure. The author Tim Powers saw this and in 1987 published a book, On Stranger Tides which borrows this iconography. Powers also decided to mix in voodoo, apparently inspired by the Louisiana connection previously mentioned. Ron Gilbert was inspired by this book (and Disney) when creating his game for LucasArts The Secret of Monkey Island in 1990, which set of an entire franchise of games. This game features the voodoo, skeletons, and undead that Powers and Disney both featured in their works. At this point, the inspiration channels circle in on themselves. Disney then makes its own pirate films, the famous Pirates of the Caribbean franchise, the first film premiering in 2003. These films, especially the first one, took a lot of inspiration from the Monkey Island franchise. Jerry Bruckheimer, the producer of these films, was originally trying to develop a direct adaptation of Monkey Island for film, but ended up working with Disney and used many of his ideas from that project for Disney's franchise. The franchise goes and adapts Power's book for the plot of their fourth film. So, two works inspired significantly by Disney in the first place become the inspiration for new Disney work, which is already based on a old piece of Disney work from the 1960s. Since Disney regularly impacts popular culture, it's no surprise that other portrayals, art, media, etc. started picking up these themes of skeletons, voodoo, and the undead and began using them in the 1990s to today. That's what I found for it's origination in popular media - if it goes back further, someone else will have to dig (I couldn't find evidence of anything significant coming before that).

TL;DR - Pirates had skulls and skeletons on their flags in the early eighteenth century, nothing else. The media started putting skulls and skeletons on stuff in the nineteenth century, but the big departure point was Disney's Pirates of the Caribbean ride in the 1960s, which inspired Tim Powers (Book: On Stranger Tides) and Ron Gilbert (Monkey Island game franchise) to pick up on more skeleton/voodoo/undead motifs, which in turned inspired Disney to use these concepts even more (the Pirates of the Caribbean franchise).