It arose in the second half of the 19th century. On the city map in 1887 it is designated as a new street, originally - Malaya Koraganovskaya, later renamed Anastasievskaya (1901-1918), in honor of Anastasia, the daughter of the Russian Emperor Nicholas II. Under this name, it is included in the list of streets compiled by the Tiflis Council in 1903.
In 1923 the street was renamed by the Soviet authorities in honor of the Russian revolutionary Sophia Perovskaya (1853-1881).
The modern name, since 1990, in honor of the Georgian Soviet scientist-linguist, academician of the Academy of Sciences of the Georgian SSR Georgy Akhvlediani (1887-1973).