The institute was established in 1951 by the Royal Swedish Academy of Sciences as the Research Station for Astrophysics on the island of Capri, Italy.
The new station is situated within the Spanish-International Observatory on the Roque de los Muchachos.
It soon became obvious that the superior astronomical climate on La Palma called for a first-class solar telescope.
During the 1990s, the daily operations of the institute gradually moved from La Palma to Stockholm.
In 2013, the institute was transferred from the Royal Swedish Academy of Sciences to its current home with Stockholm University.