Born the son of a physician in Berlin, Hückel was educated at the University of Göttingen, gaining his PhD in 1921. He worked at a number of institutions, including the Zurich Technische Hochschule and in Copenhagen, Leipzig, and Stuttgart, before taking the chair of theoretical physics at Marburg in 1937.

Initially Hückel worked with Debye on electrolyte solutions. From 1930, however, he turned his attention to organic compounds. Since Friedrich Kekulé had discovered the structure of benzene (C₆H₆) in 1865, it had continued to puzzle chemists. Kekulé had shown that the six carbon atoms of benzene were formed into a ring joined by alternating single and double bonds. Organic chemists call such molecules as benzene ‘aromatic’ thereby indicating, among other things, the molecule's great stability. Yet, double bonds normally make a molecule reactive. How, then, it was asked, can certain molecules like benzene with double bonds be so stable?

In the 1930s Hückel developed an answer to this problem based upon molecular orbital theory. Molecular orbitals are formed from overlapping atomic orbitals. Hückel proposed that the electrons of the pi-orbitals were delocalized and spread diffusely above and below the plane of the carbon ring. As this configuration was energetically more stable than placing electrons in isolated double bonds, benzene's stability followed directly from the model.

Hückel went on to generalize his model to cover other cyclic molecules containing alternating double and single bonds. Aromatic molecules were planar compounds which had precisely 4n + 2 pi-electrons, where n = 0, 1, 2, 3…. This is known as the Hückel rule. Benzene represents the case where n = 1; and n = 2 and n = 3 represent the 10 and 14 member aromatic rings of naphthalene and anthracene. For n = 0, the predicted aromaticity of a 3 member ring was confirmed in 1962 with the discovery of the cyclopropenyl cation.