He came to the throne in 1589 at the death of his father.
During his rule the Great Plague reached Eriador, and most of the people of Cardolan perished, especially in Minhiriath. The Hobbits and other peoples living in Arnor all suffered greatly, but the plague lessened as it went north, and the north of Arthedain was scarcely affected.
Still it saw the end of Cardolan, and the last prince of Cardolan was buried in the Barrowdowns in the same mound Frodo Baggins was later caught in. Evil spirits sent by Angmar passed through Rhudaur to Cardolan, and began to dwell in the Barrowdowns.
Argeleb was succeeded at his death in 1670 by his son Arvegil.