To move your characters all you need to do is use the same account when you start playing on the XB-1.
You will need a new copy of Destiny TTK (the base game and TTK) to continue playing on the XB-1 as Destiny is not part of the Backward Compatible program.
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Ah interesting, so I will have to rebuy the game AND the taken king DLC?? ugh..that's a shame but i figured. Thank you for the reply though!