Telali runs west to east, from the point where Mula Mustafe Bašeskije and Baščaršija Square meet, and then on to Vijećnica. 

It passes Telali Market and then bends slightly to head south until it meets Obala Kulina Bana.

The part of the street from Baščaršija to the end of Samardžija (now Kračule) was laid out in 1863, by order of the Ottoman governor, Topal Osman Pasha. The street was initially named after him when it was called Osman-Pašina Džada, but Sarajevans soon called it Nova Testa.

Nova Testa was used to refer to just part of what is now Telali, from Baščaršija Square to where it meets Kračule and Brodac. Until 1919 the part around Vijećnica had been called Mustaj-Pasha’s Mejdan, after Mustafa Pasha Babić, a city official who owned some property here.

Sometime around 1885, Nova Testa was renamed Telali. It is interesting to note that it was not named after the actual street criers (telali) who called out news and events, but rather after the antiques dealers and shop owners who loudly advertised (telalili, from the verb telaliti) some of the old items being sold in their shops. These merchants had been forced to relocate from Brusa Bezistan to this part of town.

After WWI, the current street took shape and was named after the BiH writer and politician, Petar Kočić.

It was called Telali during the Fascist occupation (1941–1945). When Sarajevo was liberated, it was renamed Kočićeva St. and it retained this name until 1993, when the original name, Telali, was restored.