Aghin district was established on December 31, 1937. The administrative center of the district with an area of 429 km² was the urban-type settlement of Molla Goyche. The distance from the district center to the city of Iravan is 100 km.
The territory of the district was historically included in the Shoreyel district of the Iravan Khanate, and during the Tsarist Russia it was part of the Alexandropol uezd.
The toponym is derived from the combination of the word “ağ” which means “tall, high, big” and the word “in” which means “hut, cave” in the old Turkish language. It is a toponym associated with complex terrain features.
By the decree of the Presidium of the Supreme Soviet of the Armenian SSR dated October 12, 1961, the name of the district was changed to “Ani”.
Since 1987, the native inhabitants of the district – Azerbaijanis were forced to leave their places of residence. In 1995, the district was abolished and included in the administrative territory of Shirak province of Armenia.