Elizabeth succeeded George. But the usual rules of nominalization, that should mean you use 'of'. Certainly you can use a genitive: she was George's successor. However, I would avoid it (and 'to').

As for 'throne', I'd say she was his successor on the throne, but that she was the successor to his various titles. While she succeeded to the throne, I don't think I'd say she succeeded him to the throne.

you succeed a person  ~> you are the successor of that person

you succeed to an office ~ > you are the successor to that office

I would see the throne as reference to the office as regent/queen/king. So I would use successor to the throne.