Who believed that God gave them the right to rule?

Answer 1

Almost all rulers from the Antiquity belived, and/or forced their people to believe, they had the right to rule by direct divine intervention.

Judaism, with Abram (later renamed Abraham by Yahweh), took a step further.

The followers of Abram, after the Sacred Covenant, were entitled as the "God's Chosen People", which did not happened in other ancient religions, who respected the existence of other gods.

Christians, as well as buddhists, animists or any other religion followers, are not considered as "Chosen People" by Yahweh.

Modern anthropology consider these considerations as a form of ethnocentrism.

Answer 2

That depends on what leaders you are talking about.

Some leaders, like the Pharaohs, didn't claim the right from anyone. They said that they were gods, and gave themselves the right to rule.

In other areas, the King might claim that he was chosen by god, but other leaders would govern in the king's name.

Other places claim the right is given to them by the people (in democratic-type governments).

Other people just think things need to be changed, and so making things right is the justification.

In yet other areas, power gives you the right to rule. If you can take down the current leader, then you have the right to rule because you are the strongest.