Arrhenius was born in Wijk, near Uppsala, Sweden. He originally went to Uppsala University to study chemistry, changing later to physics. Finding the standard mediocre, he transferred to Stockholm in 1881 to do research under the physicist Erik Edlund, working initially on electrical polarization and then on the conductivity of solutions (electrolytes).

At the time it was known that solutions of certain compounds conduct electricity and that chemical reactions could occur when a current was passed. It was thought that the current decomposed the substance. In 1883 Arrhenius proposed a theory that substances were partly converted into an active form when dissolved. The active part was responsible for conductivity. In the case of acids and bases, he correlated the strength with the degree of decomposition on solution. This work was published as Recherches sur la conductibilité galvanique des electrolytes (1884; Researches on the Electrical Conductivity of Electrolytes) and submitted as his doctoral dissertation. The paper's great merit was not recognized by the Swedish authorities and he was awarded only a fourth-class doctorate. Arrhenius sent his work to several leading physical chemists, including Jacobus van't Hoff, Friedrich Ostwald, and Rudolf Clausius, who were immediately impressed. This led to a period of travel and work in various European laboratories in the period 1885–91.

In 1887 van't Hoff showed that although the gas law (pV = RT) could be applied to the osmotic pressure of solutions, certain solutions behaved as if there were more molecules than expected. Arrhenius at once realized that this was due to dissociation – a conclusion confirmed by further experimental work and published in the classic paper Über die Dissociation der in Wasser gelösten Stoffe (1887; On the Dissociation of Substances in Water). The idea that electrolytes were dissociated even without a current being passed proved difficult for many chemists but the theory has stood the test of time.

This work won Arrhenius a high international reputation but only limited acclaim in Sweden. Despite this he returned to Stockholm in 1891 as lecturer at the Technical Institute and in 1895 became professor there. In 1903 he was awarded the Nobel Prize for chemistry and in 1905 he became the director of the Nobel Institute, a post he held until shortly before his death.

Arrhenius was a man of wide-ranging intellect and besides developing his work on solutions, in later life he worked on cosmogony and on serum therapy, being especially interested in the relation between toxins and antitoxins. He also investigated the greenhouse effect by which carbon dioxide regulates atmospheric temperature and calculated the changes that would have been necessary to have produced the Ice Ages.