Here is some additional info about the house moving feature:
May be limited to FCs only (this part has/hasn't been mentioned randomly, can't confirm at this point)
Will be available when Shirogane housing is purchasable.
Will put furniture into storage if there is a size change (outdoor furniture stored due to variety of yard layouts).
Initiated from an available plot's placard. (can be done at new house location)
Costs the same as outright purchasing the plot.
Transfers the personal chambers, company chest, company workshop, and airship voyage status.
Source:
http://forum.square-enix.com/ffxiv/threads/318395-4.0-Housing
Also, from an interview:
A1: Players will not be able to purchase housing at the launch of 4.0; however, they will be able to visit the housing area. The moving feature will be implemented at the same timing that the housing plots become available for purchase.
As for the steps, players will access the sign board of the plot and select the option to purchase the plot, next they will be presented with an option to move, so they will just need to select that option. You will then be required to purchase the land.
Also, there’s a new storage, so you’ll be able to store outdoor furnishings, so please use it as a storage space.
The moving feature will transfer the personal chambers, company chest, company workshop, and airship voyage status, so players will just need to prepare the fees for the new plot.
Source:
https://gamerescape.com/2017/04/28/letter-from-the-producer-live-part-xxxv-summary/