The US is playing a game of leverage, here. We saw Trump tell Japan to not escalate the row with Taiwan - but he's been more or less silent on the topic of nuclear weapons. Recently, the US approved South Korea's plan for acquiring nuclear submarines, and on the whole there's a demand from Washington for its allies/vassals to pick up more of the slack on defense related matters. To me, this is a salami slicing tactic to eventually corner China, so that Trump can step in and use it as a bargaining chip either for trade deals or the trilateral nuclear control talks the US has been trying to restart.
Japan almost certainly has back room US approval for reviewing its nuclear doctrine; otherwise the potential for an embarrassing blow back from Washington would be too much for the face-obsessed Japanese, particularly after they already suffered such a blow back just a month before. So I don't expect there will be global sanctions by the US or the EU or even South Korea for this move.
I also expect that, per salami slicing, Japan will not immediately (be allowed) to acquire its own nukes, but there will be a transition process: the US will initially just deploy nukes in Japan and claim this does not violate proliferation because they're not Japanese nukes. Then, if China continues to rise and the US continues to decline in the Pacific, those nukes will eventually be transferred to Japanese control as the US disengages. This is the process that China will have a very hard time arresting.