How Did Kratos Become the God of War?

Kratos became the God of War by killing the god who held the title. At the end of the first game he opened Pandora's Box, grew to a god's size, and ran Ares through with the Blade of the Gods. The gods of Olympus then gave him Ares's empty throne. Much later, in the Valhalla epilogue to Ragnarök, he took the title again in the Norse lands, with a very different meaning. (God of War (2005); God of War Ragnarök: Valhalla)

From servant of Ares to his enemy#

Kratos started as a mortal, though not quite an ordinary one: he was a demigod, the son of Zeus and a Spartan woman named Callisto, and he didn't know it. As a captain of Sparta he wanted glory above everything. When a barbarian horde was about to wipe out his army, he called on Ares and offered his life for victory. Ares destroyed the barbarians and bound the Blades of Chaos to Kratos's arms. (God of War (2005); God of War: Ghost of Sparta)

As Ares's servant, Kratos burned his way across Greece. Then Ares moved Kratos's wife and daughter into a temple Kratos was about to raid, and Kratos killed them without knowing. He broke his oath, and God of War: Ascension shows the Furies hunting him for it until he defeats them and is free of Ares. (God of War (2005); God of War: Ascension)

Ten years for Olympus#

Free but haunted, Kratos served the other gods for ten years in the hope that they would rid him of his nightmares. Their last task came from Athena. Ares was laying siege to Athens, and Zeus had forbidden the gods to make war on each other, so they needed a mortal to do it. If Kratos killed Ares, his sins would be forgiven. (God of War (2005))

No mortal could kill a god by himself. Kratos needed Pandora's Box, kept in a temple chained to the back of the Titan Cronos as he crawled through the desert. Kratos reached it, but Ares saw him and killed him with a thrown column. Kratos clawed his way back out of the Underworld. (God of War (2005))

Killing Ares#

Back in Athens, Kratos opened the Box. Its power filled him, and he grew to the size of a god to face Ares. The fight went against him. Ares dragged him into a vision of the night his family died, tore the Blades of Chaos from his arms and used them to kill Lysandra and Calliope again in front of him. Then Kratos saw the Blade of the Gods, the huge sword set outside the city, picked it up and killed Ares with it. A mortal had killed a god. (God of War (2005))

The gods kept their word, up to a point. Athena told Kratos his sins were forgiven, but nobody had promised to take away his memories. Kratos threw himself off a cliff into the sea. Athena pulled him out, saying the gods would not let a man who had served them so well die by his own hand. As his reward, Olympus offered him the throne Ares had left empty. Kratos climbed to it and became the new God of War. The God of War (2005) story covers the whole game. (God of War (2005))

What came of it#

Godhood didn't bring peace. In Ghost of Sparta, the new God of War goes looking for his mother and his lost brother Deimos. By the start of God of War II he is using the throne to lead Sparta's army against the cities of Greece, and the other gods are furious. (God of War: Ghost of Sparta; God of War II)

At the siege of Rhodes, Zeus tricked him into pouring the rest of his godly power into the Blade of Olympus and then killed him. Kratos came back and destroyed Olympus in God of War III, but he never sat on that throne again. The why did Kratos kill Zeus page tells that part. (God of War II; God of War III)

God of War again, in the north#

By God of War (2018) Kratos is living in Midgard and has buried the title along with his blades. He tells his son Atreus that they are both gods, but he wants nothing to do with what that meant in Greece. (God of War (2018))

The Norse gods had their own God of War, Tyr, who used the role to prevent wars rather than win them. In the Valhalla epilogue, Tyr brings Kratos to Valhalla to face his past. After repeated trials Kratos makes peace with it and accepts Freya's offer to become the God of War of the Nine Realms. Our reading is that this is the point of the whole saga: he took the title the first time by killing, and the second time by changing. (God of War Ragnarök: Valhalla)

For more on the title itself, see God of War: the divine title. (God of War (2005); God of War Ragnarök: Valhalla)