Stanojević comes from a distinguished family, a direct descendant of Prince Stanoje Mihailović from Zeoke who was killed in the Slaughter of the Knezes in 1804. Veljko's grandfather is Colonel Jeremija Stanojević (1808-1869), who was the minister of justice and education in the Principality of Serbia, president of the Supreme Court, president of the Serbian Learned Society, state advisor. His grandmother is Marija Mara Nenadović, daughter of Mateja Nenadović, grandson of Prince Aleksa Nenadović. According to his grandmother's lineage, he was related to the Karađorđević.