The person below is incorrect. The digital upgrade was extended indefinitely for Destiny, TDB and HoW so the answer is yes, you will get them free when you upgrade to Xbox One.
Bungie has not indicated whether this will occur with the Taken King so keep an eye on the weekly updates as it gets closer to launch.
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Source on the base game part? The base game and the dlc had a cutoff of Jan15th. HOWEVER, they extended the dlc "free" upgrade offer, just not the base game.
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I looked back and you are correct it makes no mention of the base game for the upgrade. I was upgraded on the base game and expansion one prior to the deadline, upgraded expansion two after the extension. So I definitely cannot confirm that the base game is upgrade able now, I made the mistake of assuming.