He came to the throne in 1349 at the death of his father.
Because the line of Kings had failed in the realms of Cardolan and Rhudaur, Argeleb claimed the Kingship of all of Arnor again, taking the royal prefix ar(a)- as a sign. He was thus not only the seventh King of Arthedain, but also the seventeenth King of Arnor.
Cardolan accepted this rule, but Rhudaur had by then fallen under control of Angmar, and resisted his rule. Argeleb fortified the hills at Weathertop, and was killed in 1356 T.A. by evil men from Rhudaur.
Argeleb I was succeeded by his son Arveleg I.