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Next week, the Baltic Flour Mills opens to the public under a new identity: the Baltic Centre for Contemporary Arts, the largest modern arts building outside London.

Though its new purpose is forward-looking, the £46m conversion is born of nostalgia. Gateshead, a dowdy sprawl, has none of the architectural drama of Grainger's Newcastle across the river, and the council was not about to give up the single iconic structure on its sorry quay.

"People knew it and were fond of it," says Dominic Williams of project architect Ellis Williams. "It was something for people to hold on to in what is a complete change in the area."

"Everybody says it would have been quicker and cheaper to knock it down and start again," agrees Chris Coulman, construction manager at contractor HBG. "But the council took the view that it was a landmark; they wanted to reuse it."

Nostalgia aside, Gateshead's idea was ahead of its time. Back in 1994, when the council launched an architectural competition for the Baltic, arts megaprojects had yet to become the standard tonic for rust-belt riversides. The National Lottery did yet not exist – although it was later to give the Baltic scheme £33m – while Tate Modern was still a rusting power station beside the Thames and few people had heard of Bilbao.

Gateshead's choice of architect was also courageous; or rather, the decision to stick with him was. Dominic Williams, then 31, had qualified as an architect only the year before and was unemployed; he produced his competition drawings in his bedroom. The council would not have known this because it was an anonymous competition, but they professed to be looking for ideas rather than experience anyway.

"The brief was one A4 sheet," Williams recalls. "They wanted to create of series of spaces for contemporary artists to work in. We came up with a very simple concept of stacking four heavyweight gallery spaces inside the existing structure, with escape routes in each of the four corners. We hollowed out the east and west facades to get daylight in, which was critical.

Plus we provided lots of views."

The simplicity of Williams' solution won the judges over. Working with his father's practice, Ellis Williams, he embarked on a job that, despite the simplicity of his proposal, was to prove tortuously difficult to execute. Although it was one of the first major lottery projects to receive funding, it is one of the last to be completed, largely because of the difficulties of building within the 40 m high brick shell.

The early stages of construction were more akin to keyhole surgery. HBG's Coulman says: "What [demolition contractor] Nuttall's left us with wasn't even a shell – just four sides of a very large building, held up by a large, temporary steel framework." To prevent the retained facades collapsing during demolition, the entire structure – including the top – had been wrapped in a steel straitjacket. "All the materials had to go over the top and down the middle, through the gaps in the frame, with tower cranes. That was a big restriction."

The four corner towers were put in first, then four post-tensioned concrete floors, each spanning the building's 50 m length and capable of supporting point loads of up to six tonnes. Once a floor had been cast, there was no way to get large materials to the levels below; so there were delays while 8 × 3 m sheets of oxidised Corten steel, which were to clad the circulation spaces on each floor, were pre-weathered in a Dutch shipyard for nine months. "That added a fair bit of time," says Coulson.

He adds: "There was a lot of problem solving on the job. A lot of it you couldn't prejudge, predesign or pre-engineer. We had to re-engineer a lot of areas during the installation stage."

A couple of changes were made to Williams' original design – a separate entrance building and an external "energy centre", which houses all the centre's services, were bolted on to free up space within the brick shell. Otherwise, his original theme has survived remarkably intact. Today, the red Gotham hulk appears little changed from the outside, save for rivers of glazing on the west and east facades and a dramatic silver viewing gallery known as "the box" gurning from one end.

Inside, though, the building is utterly transformed. The honeycomb of 148 concrete grain silos has been replaced with a sequence of white caverns providing 3300 m2 of exhibition space. The loftiest, the High Art Space, is on the fifth level. This 750 m2, 8.5 m high gallery is naturally lit by skylights and is capable of housing travelling blockbuster art shows.

Below this space are four more floors of galleries, offices, performances spaces and auditoriums. The five levels are served by staircases set at the corners, and by three panoramic elevators that race up and down the west face, affording passengers views both into and out of the building.

At the other end, a huge white sail in the shape of a beetle's back is attached flush to the wall. This can be slid back and forth to control the amount of light entering the galleries.

The building is capped by a glazed rooftop restaurant, which hovers above the uppermost gallery supported by a web of angular steel trusses. It also boasts what must be the most spectacular women's toilet in the country: the fully glazed wall offers giddying views eastward along the Tyne valley.

The building contains little in terms of architectural flourishes. Williams explains: "It wasn't really about us stamping a style on it. It's the art and the people that will bring the colour."

Instead, the designer's touch is confined to the restrained palette of materials: Corten steel, anodised aluminium and riven slate in the entrance and circulation areas; the palest Swedish pine on the gallery floors. "We were very careful not to get carried away with finishes. Quality of light is more important," says Williams.

Gateshead has changed dramatically during the Baltic's painstaking transformation. Just yards away, Chris Wilkinson's "winking eye" pedestrian bridge now loops gracefully across the boot-brown river, linking the centre's front door to the heart of Newcastle. High-rise apartments and a huge commercial and leisure complex are rising around the Baltic. A little further up the Tyne, Foster & Partners' bulbous £70m Gateshead Music Centre is getting ready to upstage them all.

It all amounts to an ambitious programme, which has been described as the South Bank of the North. Naturally, the Baltic invites comparisons with London's Tate Modern, but Sune Nordgren, its Swedish director, is having none of that. "It's an old industrial building next to a new bridge, but that's where the comparisons end," he says. "Dominic has chosen a palette of materials that goes brilliantly with the industrial feel of the building. It feels more comfortable than the Tate; it's more straightforward. The atmosphere of the building will make people feel at home."