In 1791, during the Benares State, a resident of the East India Company, Jonathan Duncan, proposed the establishment of a Sanskrit college for the development and preservation of Sanskrit Vangmaya (eloquence) to demonstrate British support for Indian education. The initiative was sanctioned by governor general Charles Cornwallis. The first teacher of the institution was Pandit Kashinath and the governor general sanctioned a budget of ₹20,000 per annum. The first principal of Government Sanskrit College was John Muir, followed by James R. Ballantyne, Ralph T. H. Griffith, George Thibaut, Arthur Venis, Sir Ganganath Jha and Gopinath Kaviraj.

In 1857, the college began postgraduate teaching. An examination system was adopted in 1880. In 1894, the famous Saraswati Bhavan Granthalaya building was built, where thousands of manuscripts remain preserved today. These manuscripts have been edited by the principal of the college and published in book form. More than 400 books have been published in a series known as Sarasvati Bhavana Granthamala.