The SweSAT originates from the 1960s ideas about increasing eligibility to universities and university colleges. Another purpose was to simplify the admission process. A selection test was thought to be a possible solution; it offered a selection method that could be used for applicants who were lacking formal grades, and could at the same time decrease the definitive impact that the grades had for applicants who had just graduated upper secondary school.
Kompetensutredningen (KU) 1965–1970 gave professor Sten Henrysson the assignment to construct a scholastic aptitude test. Prior to the 1977 university reform, the government decided that the proposed test would only be used for selection among applicants who were eligible through age and work experience, the so-called 25:4 group: those who were 25 years old, had knowledge in Swedish and English equivalent to Swedish B and English A, and had at least four years of documented work experience, were automatically given basic eligibility for university studies.
After an extensive research and development during the 1970s, largely performed under the leadership of Henrysson at the Department of Pedagogy at Umeå University, the first SweSAT was launched during the spring of 1977. The first year the test was administered at three occasions, since then it has ben administered twice per year, during spring and fall – with the exception for the pandemic years, when the spring test of 2020 was cancelled and instead two test occasions were offered both in the spring of 2021 and the spring of 2022.