The building was built as a town hall. Stromness grew quickly in the early nineteenth century on the back of the herring fishery and the Hudson's Bay Company trade, and by 1856 the population had reached the point where the area was created a police burgh. The new burgh council commissioned a neoclassical town hall, built in dressed ashlar stone and completed in 1858. The council occupied the ground floor. The Orkney Natural History Society, founded in 1837 by Stromness merchants and gentlemen-naturalists, took the first floor and opened a museum there in the same year the building was finished. In the 1920s the burgh council moved out and the society took over the whole building. It has been a museum ever since.

Stromness was for two centuries the last British port that Hudson's Bay Company ships called at before crossing the Atlantic. Generations of Orcadian men joined the company as labourers, clerks, and traders, and many of them spent their working lives in what is now northern Canada. John Rae, born on the Hall of Clestrain just outside Stromness, was the explorer who eventually established the fate of the Franklin expedition. The museum's Arctic collection reflects this connection: an Arctic medal awarded to Sir John Franklin himself, ethnographic items collected by Orcadians working for the Company, and one of only two surviving examples of the Halkett boat, a folding inflatable craft invented by a Royal Navy lieutenant in the 1840s for Arctic exploration.

Captain James Cook's third voyage, the one that took him to Hawaii where he was killed, ended in Stromness in 1780 when HMS Resolution and HMS Discovery sheltered in the harbour on their long limp home from the Pacific. Some of what the crew brought back with them stayed in the town, scattered through private collections and eventually finding its way into the museum. There are objects associated with Cook's third voyage in the Stromness Museum collection today, more than two centuries after his crew tied up at the local pier. The town's other connection to Pacific exploration came through Jack Renton, a Stromness man who survived eight years as a captive on the Solomon Islands in the 1860s before being rescued. His ethnographic collection is also on display.

Stromness sits on the western edge of Scapa Flow, the great natural anchorage where the interned German High Seas Fleet was scuttled in 1919 and where HMS Royal Oak was torpedoed by U-47 in 1939. The museum's naval history collection reflects this geography. There are artefacts recovered from the scuttling of the German fleet, fragments of ships that ended up on the seabed a few miles offshore. There is a dumaresq, a mechanical fire-control computer, recovered from HMS Vanguard, the British dreadnought that exploded in Scapa Flow in 1917 when her magazine cooked off, killing all but two of her thousand-strong crew. The Vanguard relics had been in the museum's collection for decades before researchers identified what they were.

In 2020, researchers from the National Museum of Scotland visiting Stromness identified two Egyptian faience shabti dating from 1145 to 986 BC in the collection. Nobody in Stromness had known what they were. Shabti are small funerary figurines, placed in Egyptian tombs to act as servants for the dead in the afterlife. How they reached an Orkney museum is unclear, but Orcadians travelled widely and collected widely, and the British nineteenth century was a great moment for the casual export of Egyptian antiquities. Combined with the whalebone Skara Brae figurine rediscovered four years earlier, the museum's collection includes one of the oldest known human representations from Neolithic Britain and figurines that once accompanied Egyptian dead into eternity. Not bad for a building originally meant to house council meetings.