Thomas Aquinas, Compendium of Theology

God's essence cannot be other than His existence. In any being whose essence is distinct from its existence, what it is must be distinct from that whereby it is. For in virtue of a thing's existence we say that it is, and in virtue of its essence we say what it is. This is why a definition that signifies an essence manifests what a thing is. In God, however, there is no distinction between what He is and that whereby He is, since there is no composition in Him, as has been shown. Therefore God's essence is nothing else than His existence.

Likewise, we have proved that God is pure act without any admixture of potentiality. Accordingly His essence must be the ultimate act in Him; for any act that has a bearing on the ultimate act, is in potency to that ultimate act. But the ultimate act is existence itself, ipsum esse. For, since all motion is an issuing forth from potency to act, the ultimate act must be that toward which all motion tends; and since natural motion tends to what is naturally desired, the ultimate act must be that which all desire. This is existence. Consequently the divine essence, which is pure and ultimate act, must be existence itself, ipsum esse.