Honestly, the translation posted is a bit awkward. Perhaps you can express the same thing by saying "你让我的生命变得完整"（you make my life complete）, but it doesn't exact the meaning of the original, especially the missing piece part.

For all my Chinese friends... the "puzzle" does not mean a jigsaw puzzle, 拼图. The correct translation by meaning is 你是我迷题的关鍵.

不可或缺

你是我的拼图里缺失的那一片。

在天愿作比翼鸟，在地愿为连理枝。