The museum was founded by the Yorkshire Philosophical Society (YPS) to accommodate their geological and archaeological collections, and was originally housed in Ousegate, York, until the site became too small.

In 1828, the society received by royal grant, 10 acres (0.040 km2) of land formerly belonging to St Mary's Abbey for the purposes of building a new museum.

A condition of the royal grant was that the land surrounding the museum building should be a botanic gardens and one was created in the 1830s.

On 26 September 1831, the inaugural meeting of the British Association for the Advancement of Science was held at the Yorkshire Museum.

[3] The museum was narrowly missed by a bomb during the Baedeker Blitz on 29 April 1942, though the explosion caused damage to the roof and the windows.

The curator, Reginald Wagstaffe, lived in Manor Cottage (a building adjacent to the museum) and was responsible for the subsequent clean-up effort of the debris, during which 'seven large bath-tubs' of broken glass and geological specimens were thrown away.

The £2 million scheme was largely carried out by the museum's own staff, who restructured and redecorated the interior of the building.

[11] The museum remained closed a year later, but on 28 March 2021 it announced that it had received a £18,000 'Lifeline grant' from the Culture Recovery Fund for repairs to the building façade and roof.

[13] This exhibition, and the site, closed on 31 October 2021 for the winter period in order to save resources and undertake building repairs.

There are two specimens of the extinct great auk,[18] an almost complete skeleton of an extinct moa, passenger pigeons,[19] and a large collection of Quaternary (c.125,000 years ago) specimens from the Yorkshire region including the remains of elephants, cave bears and hyena from Kirkdale Cave.

Fossils make up the majority of the collection numbering over 100,000 samples, and include important specimens from the Carboniferous, Mesozoic and Tertiary periods.

It hosted a series of weekly competitions on social media to engage with other museums in order to find the best object of a given topic, titled the 'Curator battle'.

[45] The museum won a PRCA 'Just Marketing Award' in January 2021 for the '#CuratorBattle' twitter campaign in the category of 'Best performance during COVID-19'.

[46] Analysis by York Museums Trust of this social event concluded that more than 6.2 million people saw YMT collections online due to the campaign.

[4] The Coppergate helmet was first put onto display in a permanent gallery space in 1980 following a £30,000 grant from the British Museum as part of the "International Viking Exhibition".

[54] In 2004, "Dust off the Dodo" featured collections from across the three York Museums Trust sites for the first time following its formation in 2002.

[59] The facial reconstruction of King Richard III was displayed in the museum from July–October 2013 as part of a national tour.

[63] In 2017 the museum hosted the first stage of a touring exhibition titled 'Viking: Rediscover the Legend', opened by Alice Roberts.

It is a medieval gilt-copper alloy, Limoges enamel figurine found in St Mary's Abbey, York in 1826 and acquired in 2019 from a purchase at auction.

The exhibition is collaboration with the University of York and features objects from excavations that have never been publicly display before, such as the world's oldest hunting bow.