It is one of those bright, cold mornings in which Edinburgh seems to specialise. The golden cockerel atop the spire of St Giles’ cathedral is etched against a pale blue sky, hawked spit (for good luck) has frozen on the nearby Heart of Midlothian and an early tourist pats the frost-rimed head of Greyfriars Bobby. If that faithful wee dog could see, he would surely recognise, across Chambers Street, a similar example of fidelity: the National Museum of Scotland (NMS) is about to open for the day, just as it has for the past 150 years.

“This is a hugely important moment,” says NMS director Gordon Rintoul of his institution’s 150th anniversary this year. “It’s a once-in-a-century opportunity to make a major transformation and turn this into one of the world’s great museums.”

Over a cup of tea in his top-floor office with its grand view over the city, Rintoul explains that the milestone is being marked by the last major phase of a radical overhaul. On 8 July, 10 new galleries will open, six dedicated to science and technology, the remainder to decorative art, fashion and design. This reconnects with the vision of its Victorian founders: in 1866, when it first opened, it was called the Edinburgh Museum of Science and Art. The construction of a new wing, in 1998, added Scotland’s historic treasures, and the NMS now covers everything from archaeology to zoology.

Its curators say it is the equivalent of the British Museum, V&A, Natural History Museum and Science Museum all under one roof – though detractors sneer that a museum of everything ends up as one of nothing.

“All I know is that people are voting with their feet,” says Rintoul. It is the most visited museum outside London.

The new galleries are taking shape. Five planes hang from the ceiling, among them Percy Pilcher’s Hawk glider, Britain’s oldest surviving aircraft. It’s an alarming-looking apparatus of cotton, bamboo and wire, which the Glasgow-based aviator was flying when he crashed in 1899, later dying from his injuries. The Hawk, like all 3,000 artefacts destined for the new galleries, was restored at the National Museums Collection Centre in the north of the city. This unprepossessing campus of hangars is where some 12 million objects, two million of which are insect specimens, are stored and conserved when not on display.

Heather Caven, who leads the conservation team that has spent the past four years preparing for the new galleries, describes the centre as “the beating heart of our collection” and it is not difficult to see what she means. Walk at random into one of the laboratories and you will see young women in white coats and protective gloves removing varnish from a 15th-century sculpture of Saint Sebastian, using electrolysis to reduce tarnish on a silver tongue-scraper belonging to Napoleon’s sister, and fixing the handle of a black Schiaparelli handbag. This is a place where centuries collapse under the attentive touch of the conservators.

The atmosphere throughout the centre, which is open for guided tours as part of the Science Festival in April, is one of unflappable industry. Fans of Raiders Of The Lost Ark will be reminded of the final scene, where the ark of the covenant is stored in a secret warehouse. Here, though, the mysterious object in a wooden crate is more likely to be Dolly the Sheep, the first mammal to be cloned from an adult cell. The ewe was born at the Roslin Institute, near Edinburgh, in 1996; she died in 2003, and her taxidermied remains will be a star exhibit of the new science and technology galleries.

“Dolly has been frozen at -31C for five days and brought back up to room temperature to destroy any risk of pests,” explains Chanté St Clair Inglis, the collection’s care manager, nodding towards the box. “She will live here until we move her up to the museum for installation.”

Back at the museum, the Grand Gallery – a wonderful Victorian birdcage of a room, flooded with light – is noisy with the laughter of children as they marvel at the giant skull of a sperm whale. What’s striking is the almost tangible sense that here is a place which has brought pleasure and enlightenment to several generations of Edinburgh citizens.

The novelist Alexander McCall Smith was a regular visitor while studying law at neighbouring Old College, and developed a taste for the cafe’s pies. “The National Museum is a great institution in Edinburgh life,” he says. “It expresses the character of Edinburgh rather well. Ours is a city of the mind, and this wonderful building reminds us of our intellectual history – of the spirit of enquiry that was at the heart of Enlightenment Edinburgh and that still means so much in Scotland.”

The Scotland revealed by the NMS is rich in history, and energy both creative and destructive. The ground floor relates the events of 410 million years ago, when colliding landmasses joined Scotland and England. Up a few flights of stairs is an account of the Scottish independence movement which might yet pull them apart.

For the curators, the museum is an object to be handed down and handled with care. They see themselves as custodians, links in a chain of service stretching back to the 19th century.

“This is a cultural castle defending the treasures of the nation,” says David Forsyth, principal curator of early modern Scottish history. “We are part of a long line looking after this place for the people of Scotland and beyond.”

• Chambers St, admission free, nms.ac.uk. A major new exhibition, Celts, opens on 10 March. See sciencefestival.co.uk for guided tours of the collections centre on 8 and 9 April