The correct answer to this open question is the following.
The formal Constitutional power that applies to this scenario is that the President of the United States is the Chief Diplomat and the leader of the nation. He has the power to make these kinds of decisions when he considers it necessary for the security of the country.
The informal powers or roles of the president that apply to this scenario is that the President of the United States is able to conduct foreign policy initiatives if he deems correct to get to a prompt solution of a conflict or avoid one.
Yes, the President's actions are constitutional because he is not confronting or breaking any precepts of the US Constitution. The President and the Secretary of State negotiated the agreement with North Korea to end its designs on building a nuclear weapon, and he consulted with the members of Congress to get their advice.
I agree in part, with the president's decision, but I considered necessary the signing of a formal Treaty to follow a protocol and clearly establish the conditions that back the agreements. This way, both countries would have to fulfill the agreement, no matter what happens in the future and despite any presidential changes in the United States or North Korea.
In this case, the treaty should be discussed and approved by the United States Congress.