He studied mathematics at the University of Iaşi from 1919 to 1922. In 1923, he went to the University of Göttingen, where he studied under David Hilbert. Thereafter, he went to the University of Rome, where he studied under Tullio Levi-Civita, obtaining his doctorate on November 5, 1924.
Vrânceanu returned to Iaşi, where he was appointed a lecturer at the University. In 1927-1928, he was awarded a Rockefeller scholarship to study in France and the United States. In 1929, he returned to Romania, and was appointed professor at the University of Cernăuţi. In 1939, he moved to the University of Bucharest, where he was appointed Head of the Geometry and Topology department in 1948. He retired in 1970.
During his career, Vrânceanu published over 300 articles in journals throughout the world. His work covers a whole range of modern geometry, from the classical theory of surfaces, to the notion of non-holonomic spaces, which he discovered.
He was elected to the Romanian Academy as a corresponding member in 1946, then as a full member in 1955. From 1964 he was President of the Mathematics Section of the Romanian Academy.
- Liviu Nicolescu and Gabriel Teodor Pripoae, "Gheorghe Vrânceanu—successor of Gheorghe Tzitzeica at the geometry chair of the University of Bucharest", Balkan J. Geom. Appl. 10 (2005), no. 1, 11–20. MR2209908
- Gheorghe Vrânceanu at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Gheorghe Vrânceanu", MacTutor History of Mathematics archive, University of St Andrews.