I had the same problem last month.
The only fix was to call Apple Support. Basically, the history of the account could be followed and the hacker had changed the email address and no doubt the password of my apple id. The account also showed purchases in £ so I suspect the associated country been changed as well? Apple support blocked his associated credit card, restored the account back to a date where I had last used it and we then changed the Apple ID to a new email address. I could have used the old Apple ID, effectively regaining control of it, but I wasn't attached to it and it enhanced security by changing it.
Scared myself last night as my daughetrs iphone had been associated with the old ID and she couldn't access the icloud acocunt. I'd manged to restore her iphone, although it was asking for the passowrd of the hacked Apple ID, I used the password for the 'new' ID (just the old one with a changed email) and it worked. Even after restoring the iphone, I still had to change my 'new' apple id back to the 'old' email so she could sign out of the 'old' icloud account on her phone after the restore and disable 'find my iphone'. Only then could she add her own personal icloud account and I changed my apple id back to the new email. Confused?
Point is, you will need apple support to regain control of your apple id. If you're not attched to it and want a new or modified apple id, make sure you sign out of all assoicted devices first!