Arrhenius was born on February 19, 1859 at Vik (also spelled Wik or Wijk), near Uppsala, Sweden, the son of Svante Gustav and Carolina Thunberg Arrhenius. His father had been a land surveyor for Uppsala University, moving up to a supervisory position. At the age of three, Arrhenius taught himself to read without the encouragement of his parents, and by watching his father's addition of numbers in his account books, became an arithmetical prodigy. In later life, Arrhenius enjoyed using masses of data to discover mathematical relationships and laws. At age 8, he entered the local cathedral school, starting in the fifth grade, distinguishing himself in physics and mathematics, and graduating as the youngest and most able student in 1876.

At the University of Uppsala, he was unsatisfied with the chief instructor of physics and the only faculty member who could have supervised him in chemistry, Per Teodor Cleve, so he left to study at the Physical Institute of the Swedish Academy of Sciences in Stockholm under the physicist Erik Edlund in 1881. His work focused on the conductivities of electrolytes. In 1884, based on this work, he submitted a 150-page dissertation on electrolytic conductivity to Uppsala for the doctorate. It did not impress the professors, like Per Teodor Cleve, and he received a fourth class degree, but upon his defence it was reclassified as third class. Later, extensions of this very work would earn him the Nobel Prize in Chemistry.

There were 56 theses put forth in the 1884 dissertation, and most would still be accepted today unchanged or with minor modifications. The most important idea in the dissertation was his explanation of the fact that neither pure salts nor pure water is a conductor, but solutions of salts in water are. Arrhenius' explanation was that in forming a solution, the salt dissociates into charged particles (which Michael Faraday had given the name ions many years earlier). Faraday's belief had been that ions were produced in the process of electrolysis; Arrhenius proposed that, even in the absence of an electric current, solutions of salts contained ions. He thus proposed that chemical reactions in solution were reactions between ions.

The dissertation was not very impressive to the professors at Uppsala, but Arrhenius sent it to a number of scientists in Europe who were developing the new science of physical chemistry, such as Rudolf Clausius, Wilhelm Ostwald, and J.H. van 't Hoff. They were far more impressed, and Ostwald even came to Uppsala to persuade Arrhenius to join his research team. Arrhenius declined, however, as he preferred to stay in Sweden for a while (his father was very ill and would die in 1885) and had received an appointment at Uppsala.

In an extension of his ionic theory Arrhenius proposed definitions for acids and bases, in 1884. He believed that acids were substances which produce hydrogen ions in solution and that bases were substances which produce hydroxide ions in solution.

Arrhenius next received a travel grant from the Swedish Academy of Sciences, which enabled him to study with Ostwald in Riga (now in Latvia), with Friedrich Kohlrausch in Würzburg, Germany, with Ludwig Boltzmann in Graz, Austria, and with van 't Hoff in Amsterdam.

In 1889 Arrhenius explained the fact that most reactions require added heat energy to proceed by formulating the concept of activation energy, an energy barrier that must be overcome before two molecules will react. The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds.

In 1891 he became a lecturer at the Stockholm University College (Stockholms Högskola, now Stockholm University), being promoted to professor of physics (with much opposition) in 1895, and rector in 1896.

He was married twice, to his former pupil Sofia Rudbeck (1894 to 1896), with whom he had one son, and to Maria Johansson (1905 to 1927), with whom he had two daughters and a son.

About 1900, Arrhenius became involved in setting up the Nobel Institutes and the Nobel Prizes. He was elected a member of the Royal Swedish Academy of Sciences in 1901. For the rest of his life, he would be a member of the Nobel Committee on Physics and a de facto member of the Nobel Committee on Chemistry. He used his positions to arrange prizes for his friends (Jacobus van't Hoff, Wilhelm Ostwald, Theodore Richards) and to attempt to deny them to his enemies (Paul Ehrlich, Walther Nernst). In 1901 Arrhenius was elected to the Swedish Academy of Sciences, against strong opposition. In 1903 he became the first Swede to be awarded the Nobel Prize in chemistry. In 1905, upon the founding of the Nobel Institute for Physical Research at Stockholm, he was appointed rector of the institute, the position where he remained until retirement in 1927. He became a Fellow of the Royal Society in 1910.

Eventually, Arrhenius' theories became generally accepted and he turned to other scientific topics. In 1902 he began to investigate physiological problems in terms of chemical theory. He determined that reactions in living organisms and in the test tube followed the same laws. In 1904 he delivered at the University of California a course of lectures, the object of which was to illustrate the application of the methods of physical chemistry to the study of the theory of toxins and antitoxins, and which were published in 1907 under the title Immunochemistry. He also turned his attention to geology (the origin of ice ages), astronomy, physical cosmology, and astrophysics, accounting for the birth of the solar system by interstellar collision. He considered radiation pressure as accounting for comets, the solar corona, the aurora borealis, and zodiacal light.

He thought life might have been carried from planet to planet by the transport of spores, the theory now known as panspermia. He thought of the idea of a universal language, proposing a modification of the English language.

In his last years he wrote both textbooks and popular books, trying to emphasize the need for further work on the topics he discussed.

In September, 1927, he came down with an attack of acute intestinal catarrh, died on 2 October, and was buried in Uppsala.