Born in Timisoara, Romania, Balaban graduated as a chemical engineer from the Polytechnic University in Bucharest (UPB), then continued his studies in radiochemistry, and obtained his Ph. D. in 1959, followed by a D.Sc. in 1974.
In 1961 he founded the laboratory for Isotopically Labelled Compounds at the Institute of Atomic Physics in Bucharest. Between 1967 and 1970 he was a Senior Research Officer at the International Atomic Energy Agency in Vienna, Austria. From 1970 until 2000 Balaban lead the Bucharest Polytechnic University and taught general and organic chemistry to many generations of students. Since 2000, he has been Professor of Chemistry at the Texas A&M University in Galveston. He has been invited as visiting professor to a high number of universities (Harvard, École Normale Supérieure, etc.) all over the world.
Balaban's diverse research interests include experimental organic and bio-organic chemistry, in particular reaction mechanisms, and free radicals.
He has been recognized for his remarkable achievements in mathematical chemistry, in particular in the chemical applications of graph theory and chemical topology. He has introduced many new topological indices and other molecular descriptors used for the molecular modelling of compounds. One of these indices is known as the Balaban index, and is used successfully in drug design.
During his career he has been a member in the editorial board of ten professional periodicals; and along with his books, his publication include seven hundred papers published in peer-reviewed journals. He is a member of the Romanian Academy of Science and honorary member of several other academies.