The Mechanics' Institution of Hobart, Van Diemen's Land Agricultural Society and Van Diemen's Land Scientific Society had each attempted to found a museum earlier than this date, the most successful of these being the Mechanics' Institution, but little record remains of what happened to these efforts.

In 1855 the Lady Franklin Museum, founded in 1842 at Acanthe Park (now Lenah Valley), sold its fittings and collection to the Royal Society and these were added to the TMAG.

[4] In 1861 after a number of years, funding was acquired from the state government to construct a museum on the corner of Argyle and Macquarie Streets, and the Royal Society hosted an architectural contest.

The Museum was completed by 1862 and a celebratory art exhibition was hosted by Morton Allport, Henry Hunter and a Captain F. E. Chesney.

[5] Adye Douglas, Premier of Tasmania, was elected Chair of the Board and Alexander Morton was reelected curator and secretary[5] with an annual salary of £200.

[6] Since then the Museum has expanded to occupy all the buildings in the block, including the 1810 Commissariat Store, and the 1902 Customs House facing Davey Street.

[9] The Royal Society of Tasmania founded the museum, donating much of its collection, and continues to loan a significant number of pieces.

[10] In addition to the main campus, TMAG includes three external sites: a herbarium, a storage and research facility, and the Moonah Workshop.