How do I politely decline a professor who's really keen on having me for a PhD position?
I would just reply that you thank him for his interest but that it isn't possible to work together at this time. But suggest that you would be honored/happy to stay in contact for the future if your fields of interest intersect. 

Over the long run you want to build up a set of contacts like this and you have an opportunity to start it. He might be a future source of advice on your research or your career. But such contacts need to be nurtured. 

I would, however, hold off on such a reply until you have a firm and accepted position elsewhere.