There was a debate on Neil Gaiman’s website last year, as to whether Neil would be eligible for the Newbery medal. Seeing as they’ve just given it to him, I’d guess Neil was correct in his assumption that he fulfilled the criteria. Resident in the US, I believe, but no need for citizenship.
Philip Pullman was asking about this on the Rutgers’ Child Lit list yesterday, but I assume without any expectation that he would ever be Newbery medalled. Apparently Philip is a fan of The Graveyard Book, so I’m in good company.
Another debate seems to be over giving the Newbery to someone as high profile as Neil, but you can’t always seek out the obscure and penalise the successful. Even JKR was awarded the odd prize in her time.