Veljković was born in Štrpce, SAP Kosovo, SR Serbia, SFR Yugoslavia.[2] He holds a degree in economy.[3]
In May 2020, Veljković was appointed head of the Office for Communities by Prime Minister Albin Kurti, replacing Nenad Rašić who resigned earlier.[2][3][4] Following his appointment, it was revealed that some years earlier Veljković had posted songs dedicated to Ratko Mladić on his Facebook account, raising controversy.[5]
Veljković was an MP candidate of Civic Initiative for Freedom, Justice and Survival (GI SPO) in the 2021 Kosovan parliamentary election.[6] On 3 February 2021, Veljković was detained by Kosovo police in Štrpce because the member of the local electoral commission Emran Avrdi accused him of making death threats towards him.[7] During the election campaign, Veljković and Rašić, together with Albin Kurti, visited Štrpce.[8] GI SPO only won 1,508 votes or 0.17% of the popular vote, hence Veljković failed to get elected to the Assembly of Kosovo.[9] Veljković, however, managed to enter the Assembly on 17 November 2022 as a replacement for one of the Serb List (SL) MP's who resigned on 7 November 2022.[10]