In Geoffrey's History of the Kings of Britain, Brutus encounters Corineus near the Tyrrhenian Sea. The people led by Corineus descend from Trojans who accompanied Antenor after the fall of Troy; they are not simply survivors arriving directly from that war. Recognising a shared ancestry, the two groups join forces. Corineus accepts Brutus as leader while retaining a prominent place among the migrants. Geoffrey combines his strength with a measured manner in counsel, making him both a champion and the head of a community seeking a lasting home.

Their progress through Gaul brings them into conflict with Goffarius Pictus, king of Aquitaine. A dispute over hunting develops into armed confrontation. Corineus becomes a dominant figure in the fighting, exchanging his sword for an axe and performing feats on a scale characteristic of heroic legend. Later, when larger forces threaten the Trojans, he and Brutus use a divided attack to overcome their opponents. The campaign is costly despite their successes, and the migrants eventually provision their ships and sail towards the island of Albion.

After the landing, Brutus establishes his people and Corineus receives a share of the country. Geoffrey places the naming of Cornwall and Corineus's choice of that region before the famous wrestling match, not as a reward granted afterwards. The chronicler links the regional name with Corineus and with the peninsula's horn-like shape. This is a legendary explanation of a place-name rather than independent linguistic proof. Corineus is attracted to the region because of the giants there, whose strength offers a challenge suited to his own.

At a celebration near the landing place, Gogmagog and twenty other giants attack the settlers. The Trojans overcome the attackers but spare Gogmagog so that Corineus can wrestle him. During the struggle the giant breaks three of the champion's ribs. Corineus then raises his opponent, carries him towards a high coastal rock and hurls him into the sea. Geoffrey calls the place Gogmagog's Leap. Later tradition associates the episode with the Plymouth landscape, but the chronicle's feat is not evidence for a historical duel or a securely located giant's grave.

Corineus also protects the position of his daughter Gwendolen. When Locrinus wishes to favour Estrildis instead of honouring the arranged marriage, Corineus confronts him and insists that the promise be kept. Locrinus marries Gwendolen while secretly maintaining his other relationship. Only after Corineus dies does he openly reject his wife, provoking her retaliation. Later works, including the play Locrine, develop the family drama in different ways. Across these retellings Corineus remains the founder whose physical strength and family authority help establish the legendary order of Cornwall, even though neither can prevent the conflicts of the next generation.