This is one of the things that is annoying most of the player base and is promised over and over again. This was first mentioned way back in 2013 and was told "we would have this after patch 2.2". Here we are now over 3 years later and still getting fed the same line.

http://forum.square-enix.com/ffxiv/t...ry-(10-30-2013)

1:34:37
Q: Can you move or reconstruct your house?
A: We're planning to have this after patch 2.2.
Until I see an actual date I wont hold my breath.