It is probably the Surium of Classical authors, specifically Pliny the Elder (AD 23-79), who place it in the eastern part of Colchis, towards Iberia.

Strategically located at the entrance into the Borjomi Gorge and guarding the road from eastern to western Georgia, Surami became a heavily fortified town in the 12th century.

After the prince's surrender in 1745, the fortress was demolished, but later restored and exploited by the Russo-Georgian troops in anti-Ottoman operations during the Russo-Turkish War (1768–1774).

After the Russian annexation of Georgia in 1801, Surami housed a military post and was later popularized as a mountain climatic resort.

The Museum consists of the house where the poet died, a library and Ukrainka's monument authored by the Georgian sculptor Tamar Abakelia (1952).