Commentaries:
Barnes' Notes
For the kingdom is the Lord' s - The dominion belongs of right to Yahweh, the true God. See Matthew 6:13; Psalms 47:7-8.
And he is the governor among the nations - He is the rightful governor or ruler among the nations. This is an assertion of the absolute right of Yahweh to reign over the nations of the earth, and the expression of an assurance on the part of the Messiah that, as the consequence of his work, this empire of Yahweh over the nations would be actually established. Compare Daniel 7:13-14, note; Daniel 7:27, note; and I Corinthians 15:24-28, notes.
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