Blizzard have clarified how the white and grey transmog items will work once patch 10.0.5 arrives.

White and Grey (Source)


Common (white) and Poor (grey) quality equipment can now be used for transmogrification. These items will now become bind-on-equip.

If you already possess these items, they will become bind-on-equip, and you’ll just need to equip them to obtain the appearance.

Items that you do not have in your inventory when the patch goes live will have to be obtained and equipped for the system to register them.