He was the son of Baldwin, Lord of Neghir (a nephew of Hethum I of Armenia), and second cousin of Constantine II.

He attempted to wipe out all rival claimants to the throne, giving orders to kill Constantine II's nephews, Bemon and Leo, but before the murders could be carried out they escaped to Cyprus.

During his rule, the Armenian Kingdom of Cilicia was reduced by Mamluk raids and conquests.

Constantine was the first husband of Maria, daughter of Oshin of Corycos and Joan of Taranto.

Upon his death from natural causes he was succeeded by his cousin Constantine IV.