Any DLCs you buy on the 360 will transfer over to the One.
I had this happen for me personally when I transferred to the One shortly after House of Wolves released.
However - you WILL have to buy the base Destiny game again for the One to be able to play. For some reason your copy of Destiny will not transfer over, but your DLCs, Saves & Special packages will.
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I just checked the weekly update for any info on the eligibility to upgrade from Xbox 360 to Xbox One without any extra cost and it appears that the upgrade program does NOT apply to "The Taken King" DLC. So, we will need to buy 2 versions if we want to play on last gen and current gen consoles. Here is the link: [url=https://www.bungie.net/en/Help/Troubleshoot?oid=13347][/url] I'm upset by this... I don't understand why they couldn't allow it.
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Ok, Cool! Thanks for letting me know. I guess. I assumed it was another annual game release or something instead of DLC.