Veljovic was born in 1958 in Svilanovo. He graduated from the Faculty of Law in 1983 and was employed in the Kragujevac Secretariat for the Interior in 1986 in the department for fighting crime. In 2000, he became head of the department for control of legality in the criminal police headquarters.
From mid-2003 until February 2005, he worked in the general inspector’s service of the state security and in May 2005 he was appointed head of criminal police headquarters. He was promoted to general-major in March 2006. He is married, with two children.