Veljko Petrović was born in Sombor. His father became an Eastern Orthodox monk, Gerasim Petrović, after his wife died. After graduating from high school in his home town, Veljko went to Budapest to study law. From 1906 to 1907 he was co-editor of Croatia, a Croatian-Serbian magazine for social, political and economical studies, founded in Budapest. Because of his nationalistic attitude he was forced to move to Belgrade, where he participated as a war correspondent in both Balkan Wars and World War I, and wrote poetry. Between the wars he was active in cultural and educational affairs and continued to be so until his death in Belgrade in 1967.
He first came to the attention of literary critics for his patriotic poetry, Rodoljubive pesme (Patriotic Poems, 1912) and Na pragu (On the Threshold, 1914). Afterwards, he turned to the short story and remained in the genre. His patriotic poetry avoids bombastic phrases and inflated pathos; it is rather a somber, realistic appraisal of his country and its past and a declaration of sincere, unconspicuous love for it. In his numerous stories he depicts, for the most part the life of the Serbs in Vojvodina, first under the multi-national Austro-Hungarian Empire, and later, part of the triune Kingdom of Serbs, Croats and Slovenes, an unlikely confederacy of Slav states that went on to change its name again to the Kingdom of Yugoslavia and again after World War II when the communist usurper took over. Petrović's colorful description of the Vojvodina peasants and small-town folk offer a rich thematic canvas of a teeming life, replete with national, social, and moral problems. He has also written love stories and many stories for children.

With Mileta Jakšić, according to critic Jovan Skerlić, he is considered to be one of the leading poets of Post-Modernism in Serbian literature (only after being influenced by modernism in his youth). Veljko wrote mostly about Vojvodina (like Mileta Jakšić) its ambience and people. His many functions and memberships of various boards and committees included the chairmanship of Novi Sad's Matica srpska, from 1953 to 1956, followed by his election as the institution's lifelong president. He was a member of the Serbian Academy of Sciences and Arts, and president of Srpska knjizevna zadruga in Belgrade. From 1944 until his retirement in 1962, he was the director of the National Museum, Belgrade. His collection of short stories are: Varljivo Prolece (Changing Spring, 1921); Bunja i drugi iz Ravangrada (Bunja and Others from Ravangrad, 1921); Pomerene savest (Demented Consciences, 1922); Iskusenja (Temptations, 1924); Izdanci iz zapaljena grma (Shoots from a Burning Stump, 1932); and Prepelica u ruci (A Quail in the Hand, 1948). He is best remembered, however, for Dah (Breath). He was the author of numerous magazine articles and studies on literature and art. He was one of the few to receive the coveted Yugoslav Writer's Association award.