A mage of the dark arts who seeks the powers of the void, but in reality is a tree embodied by the evil wills of man.
—Dissidia 012 description
A magus of supreme darkness, born from a great evil sealed into a tree.—Dissidia Final Fantasy description
Exdeath is a powerful warlock; he was once a tree used to imprison hateful spirits in the Great Forest of Moore. All of the evil souls would soon merge into Exdeath, whose goal would be to control the Void. Once he controls the Void, he will return the world to a state of nothingness.
Exdeath: “Mwah-hahahaha! Gaining knowledge in what I do changes nothing for you! My ambition exceeds your petty plots. What I desire is…a true ending.”Exdeath: “I will wait until you are gone– before I return the world to the Void.”
Exdeath has no true motivation for his evil, beyond simply ending existence. Chaos most likely summons Exdeath to World B after his first defeat to Bartz on Galuf’s world. During the merger of Galuf’s and Bartz’s world, the Crystals shatter; the blinding white light signifies the

Eventually, he seizes control of the Void, sealed away in the Interdimensional Rift. The Interdimensional Rift bizarre mishmash of dimensions between worlds, where Bartz and Gilgamesh stumble upon World B.
Exdeath resides in the Interdimensional Rift on the Merged Worlds. He could have used the Interdimensional Rift as a portal to find himself in World B as well. Of course, this would be before the Void consumes and transforms him into Neo Exdeath; he does not change forms in World B.