That's a good question. The shortest answer I can provide is that it's been around since practically day one, just look at period publications such as Buccaneers of America or A General History of the Most Notorious Pirates. As to when the modern versions of pirate romanticism began, one could argue that it started in the late nineteenth century when the tropics were "tamed" and made appealing to Americans and European. Also, writers of stories for young boys began crafting pirates into suitable opponents for the heroes of the story. Another point of disembarkation for pirate romanticism could be around the 1980s when scholars began pushing the "radical pirate" interpretation of historical piracy, even though the historical record, when placed in it's proper context, did not coincide with the radical pirate historians' anti-capitalist, libertine, equality for all, democracy founding version of the pirates.

If you want to see how the history differs from the romanticized version of the pirates, you luckily caught me right when I completed a post on my blog, "Colonies, Ships, and Pirates", concerning what life was like in pirate-occupied New Providence. It's entitled, "The Strongest Man Carries the Day," Life in New Providence, 1716-1717.