Kobayr was built on a shelf of a gorge by the princes of the junior Bagratuni branch, Kyurikids in 1171. The monastery was later acquired by the Zakarids and converted into a Chalcedonian monastery. Many of the writings in the monastery are written in Georgian.
The monastery is being fixed and paid for by the government of Armenia with the help of the government of Italy. The ruins of the main church in the monastery contain frescoes of Christ and the twelve apostles as well as the Church fathers and other Christian figures.