The Drexel Institute of Art, Science, and Industry was founded in 1891 and first opened to students in 1892. At first, the institute consisted of the following eleven departments:

After a great deal of administrative reorganization under the first president, James MacAlister, the departments were consolidated by President Hollis Godfrey into four schools in 1914. In the School of Engineering, the curricula offered through the scientific and technical departments became the basis for four-year degree-granting courses of study, while the courses offered in mechanic arts became a lower school offering non-degree or preparatory courses of study. The departments of domestic economy, business, and lectures and evening classes became the School of Domestic Science and Arts, the Secretarial School (later the School of Business), and the Evening School, respectively. The library school was discontinued in 1914 and reopened in 1922. The Art Department had closed in 1905, except for the Department of Architecture, which also closed in 1914.

When the Drexel Institute opened, all of its classrooms and facilities were housed in a single building, the Main Building, which was designed and constructed by the noted Philadelphia architectural firm of Wilson Brothers and Company. The building was completed in 1891. A second building, East Hall (later Randell Hall), was built in 1901.

Athletic activity began at Drexel with physical education, which was required and taught by the Department of Physical Training, while competitive athletics were organized informally by students. An athletic association for men’s sports, responsible for organizing games and fostering student interest in athletics, was established in 1895; a women’s athletic association was formed sometime before 1908. President Godfrey began a policy of official support and funding for competitive sports in 1914. Sports played in the early days of the Drexel Institute included football, basketball, baseball, tennis, riflery, track, and possibly crew for men and basketball and riflery for women. Other important features of student life include fraternities and sororities, beginning in 1900; student publications such as the Eccentric (precursor to the Lexerd) and the Triangle (founded in 1926); and extracurricular activities such as bands, orchestras, glee clubs, and theatre.