Kolbe, the son of a clergyman from Göttingen, in Germany, was the eldest of 15 children. He studied under Friedrich Wöhler at Göttingen and then, in 1842, went to Marburg as Robert Bunsen's assistant and learned his method of gas analysis. In 1845 he went to London to work as Lyon Playfair's assistant on the analysis of mine gases for a commission set up to investigate recent explosions in coal mines. He was professor of chemistry at Marburg from 1851 until he moved to Leipzig to succeed Justus von Liebig in 1865.

Kolbe made a number of advances in organic chemistry. He was the first to synthesize acetic acid from inorganic materials (following Wöhler's synthesis of urea). The Kolbe method is a technique for making hydrocarbons by electrolysis of solutions of salts of fatty acids. He also produced a Textbook of Organic Chemistry (1854–60), which collected together all the methods of preparing organic compounds and in 1854 he edited Liebig and Wöhler's Dictionary of Chemistry.