This sadly depends on your retailer.
I am not sure if consoles have the options to buy digitally from the ZOS store, if you do then it'll open up on June 6th to use.
If you buy the physical copy you'll have to speak with the retailer to see when it would be with you.
Additionally you could buy a copy of the base game now and then the Morrowind upgrade, that way you can enjoy the game now and have Morrowind to look forward to as a new area in a few months.