Founded under the will of John Anderson (1726-1796), Professor of Natural Philosophy in the University of Glasgow, Anderson's (or the Andersonian) Institution was established in 1796. The intention was to establish four faculties, of Arts, Medicine, Law and Theology, though Law and Theology were never founded. Courses in chemistry, natural philosophy, mathematics and other scientific subjects, together with English, rhetoric, music and art were offered. In keeping with John Anderson's views, classes were offered for the mechanics of the city. Among the early professors were eminent men such as Thomas Garnett, George Birkbeck and Thomas Graham. In 1828 the institution changed its name to Anderson's University and in 1877 it changed again to Anderson's College, as it lacked a royal warrant to function as a university.

An important part of the institution (founded in 1799) was Anderson's Medical School, of which David Livingstone was perhaps the most famous alumnus. In 1887, the Medical School became an independent institution, and it eventually merged with the University of Glasgow Medical Faculty in 1947.

Anderson's College merged with other institutions in 1887 to become the main component in the Glasgow and West of Scotland Technical College.