Allahverdi district was established on September 9, 1930. The administrative center of the district with an area of 1111 km² was the city of Allahverdi. The distance from the district center to the city of Iravan is 191 km. The Tona River flows through the district center.
The territory of the district was historically included in the Loru district of the Iravan Khanate, and during the period of Tsarist Russia, it was included in the Borchali district of the Tbilisi governorate.
The toponym was formed on the basis of the ethnonym “Allahverdi” belonging to the Borchali Turkic tribe.
By the decree of the Presidium of the Supreme Soviet of the Armenian SSR dated September 19, 1969, the name of the district was changed to “Tumanyan”. It was renamed “Tashir” in 1991.
Since 1987, the native inhabitants of the district – Azerbaijanis were forced to leave their homeland. In 1995, the district was abolished and included in the administrative territory of Lori province of Armenia.