Veličković graduated from the Faculty of Architecture at Belgrade University. From 1963 to 1966, he was an assistant in Krsto Hegedušić’s master workshop in Zagreb. In 1965, he was honoured with a prize at the Biennale in Paris, where he moved to the following year and continues to live and work to this day. Veličković gained public attention in 1967 with an exhibition at the Galerie du Dragon in Paris, which established him as one of the leading artists of the Narrative Figuration art movement. In 1983 he was elected professor at the École nationale supérieure des Beaux-Arts in Paris, and taught there until 2000. In 1985 he was elected a member of Serbian Academy of Sciences and Arts (SANU). He was honoured with the highest French award in the field of culture and arts, the Commander of the Ordre des Arts et des Lettres. His paintings were exhibited in many countries in Europe and Americas since 1951.

Since 7 December 2005 he is a member of Académie des Beaux-Arts, section I, seat number 7.