The Asiatic Society of Mumbai was founded by Sir James Mackintosh, a distinguished lawyer, jurist and public figure in England who became the Recorder or the King’s Judge for Bombay. Known then as the Literary Society of Bombay, it met for the first time on November 26, 1804.
The Literary Society purchased the collections of the Medical and Literary Library, a private library founded in 1789, and this formed the nucleus of the Library.  In 1826, the Literary Society merged with the recently established Royal Society of Great Britain and Ireland (RAS) as its Bombay Branch of the Royal Asiatic Society (BBRAS).  In 1830, it moved into the Town Hall Building, towards the construction of which it made a contribution of Rs 10,000/-.  In 1873, the Geographical Society of Bombay and in 1896 the Anthropological Society of Bombay merged with the BBRAS, bringing in their collections. 
In 1841, the Society started publishing a journal titled 'Journal of the Bombay Branch of the Royal Asiatic Society' which continues to be published under the name 'The Journal of the Asiatic Society of Mumbai.'  That was also the year the Society began admitting Indians as members.