God is not only his essence, as shown above, but also his existence. This can be shown in many ways. First, whatever is in something that is other than its essence must be caused either by the principles of the essences, as in the case of proper accidents following from the species (as the ability to laugh follows from being human and is caused by the essential principles of the species); or by something external (as heat is caused in water by fire). Accordingly, if the very existence of a thing were other than tis essence, then it would be necessary for its existence to be caused either by something external or by its own essential principles. But it is impossible for existence to be caused solely by the essential principles of a thing, because no thing suffices as the cause of its own being if its existence is caused. It therefore follows that anything whose existence is other than its essence must be caused to exist by something else. This cannot be said of God, however, since we call God the first efficient cause. It is therefore impossible in God that existence be other than essence.
Second, existence is what makes every form or nature actual, for neither goodness nor humanity is signified in actuality except inasmuch as we signify that it exists. Accordingly, it follows that existence itself is related to an essence that is distinct from it as actuality is related to potentiality. So since there is no potentiality in God, as shown above, it follows that in God essence is not other than existence. Thus God’s essence is God’s existence.
Third, just as that which has fire but is not itself fire is on fire through participation, so too that which has existence but is not itself existence is a being through participation. But God is his essence, as shown above. Thus if God were not identical with his existence, God would be a being through participation rather than essentially. This would mean that God is not the first being, which is absurd to say. Accordingly God is his existence and not only his essence.
[From Summa Theologiae, Question III, Article 4, in The Treatise on the Divine Nature, by St. Thomas Aquinas]