Alfvén, who was born in Norrkoeping, Sweden, was educated at the University of Uppsala where he received his PhD in 1934. He subsequently worked at the Royal Institute of Technology, Stockholm, where he served as professor of the theory of electricity (1940–45), professor of electronics (1945–63), and professor of plasma physics (1963–73).

Alfvén is noted for his pioneering theoretical research in the field of magnetohydrodynamics – the study of conducting fluids and their interaction with magnetic fields. This work, for which he shared the 1970 Nobel Prize for physics with Louis Néel, was mainly concerned with plasmas; i.e. ionized gases containing positive and negative particles. He investigated the interactions of electrical and magnetic fields and showed theoretically that the magnetic field, under certain circumstances, can move with the plasma. In 1942 he postulated the existence of waves in plasmas; these Alfvén waves were later observed in both liquid metals and ionized plasmas.

Alfvén also applied his theories to the motion of particles in the Earth's magnetic field and to the properties of plasmas in stars. In 1942, and later in the 1950s, he developed a theory of the origin of the solar system. This he assumed to have formed from a magnetic plasma, which condensed into small particles that clustered together into larger bodies. His work is also applicable to the properties of plasmas in experimental nuclear fusion reactors. Alfvén's books include Cosmical Electrodynamics (1950), which collects his early work, On the Origin of the Solar System (1954), and On the Evolution of the Solar System (1976, with G. Arrhenius).

In his later years Alfvén argued against the current orthodoxy of the big-bang theory of the origin of the universe. Space, he argued, is full of immensely long plasma filaments. The electromagnetic forces produced have caused the plasma to condense into galaxies. As for the expansion of the universe, he attributed this to the energy released by the collision of matter and antimatter. Whereas Alfvén's critics charged him with vagueness, he responded by arguing that cosmologists derive their theories more from mathematical considerations than from laboratory experiments.