It was 10 years in the making, it cost a fortune and it lost its architect along the way. But the BBC's new Broadcasting House is finally finished. Jonathan Glancey gets an early look inside

This is a daunting, vaulting space. I am standing in the News Room of the BBC's gleaming and much-talked-about new building. With its vast pillars, spiralling staircases, and towering lift shafts painted red and orange, this cavernous, boldly modern space seems more like a submarine dock, the sort of place you might expect a James Bond shoot-out to take place, rather than somewhere for Huw Edwards to calmly read the news.

The News Room may take up most of the basement and ground floor of the main wing of the £1bn new addition to Broadcasting House, but it is a surprisingly bright space, thanks to the fact that its glass ceiling is all but invisible, vanishing into the crevice-like atrium. The effect is striking, although the experience of looking up from a desk might be a little vertiginous: let's hope Jeremy Paxman doesn't develop a crick in his neck. The idea is to induce a sense of drama and urgency into the building and so, I suppose, into the news operation – dramatic and urgent enough, you would have thought, without the need for help from architecture.

Over the last 10 years or so, amid rising controversy, the BBC has spent £1.04bn refurbishing and extending its ocean-liner-like HQ in central London. Although it is still being fitted out, the new-look Broadcasting House, three linked buildings clustered around a new public courtyard, is now pretty much complete. In 2013, some 5,000 journalists, programme-makers, managers and other staff will be shipped here from historic BBC buildings elsewhere, including Television Centre in Shepherd's Bush and Bush House in Aldwych, home of the World Service. The aim of this eye-popping expenditure is to bring TV, radio and online operations together, increasing efficiency while reducing costs, by getting rid of a plethora of properties across town.

As well as being refurbished, the original art deco Broadcasting House, designed by George Val Myer and home to BBC radio since it opened in 1932, has gained a muscular, Portland stone and glass-clad wing. Not only does it house offices and studios, it also faces All Soul's Church, a splendidly elegant Regency creation by John Nash. To the north sits the massive news and studio complex, a dramatic hub containing the News Room; its interior is destined to become highly familiar, as it will serve as a backdrop to the likes of Nick Robinson, Hugh Pym and Stephanie Flanders bringing you the news – and giving you a hint of where at least some of that billion pounds has gone. Visitors will be able to watch news gathering in action from a glazed gallery above.

The News Room certainly packs a punch: tiers of glazed offices surround it from great heights, some floors reached by those balletic spiral stairs crafted in oak, glass and steel. There is direct access from there to six new TV studios, suspended on enormous steel springs, designed to counteract vibrations caused by the Bakerloo Line.

The project has quite a history. It had been mooted when John Birt was the BBC's director-general in the 1990s, but finally took shape in 2002, after a much-heralded architectural competition when Greg Dyke was at the helm. Since then, Mark Thompson has taken over, while the original architects – MacCormac Jamieson Prichard (MJP), a medium-sized practice best known for high-quality designs for colleges – were replaced in 2005 by experienced corporate giant Sheppard Robson. Costs have risen, completion dates have been extended, and the BBC's reputation as an architectural client has been damaged.

What happened was that the BBC, reflecting its position as a nurturer of the arts, wanted to spark its very own architectural renaissance. Then, at some point, management decided it had been aiming too high; costs were cut, ambitions lowered. This hit the News Room hardest. MJP's original design was sensational: a magnificent space supported and framed by enormous tree-like columns, with branches spreading around the room, to even out the load of all the floors above. It had the look of the command centre of an intergalactic spaceship, even though MacCormac was making references to revered architects such as John Soane, as well as dreaming up the future. It would have been a thrilling place not just to work in but to look into – from above, or from the comfort of your own living room. The problem was that this was a demanding design. The BBC wanted compromise, and the architect refused. Richard MacCormac went, bound to silence.

The artwork you can walk over

What stands there now may well be practical, and doubtless works, yet it's hard not to feel that the heart of the building was ripped out before it had even started to beat. Still, Sheppard Robson maintain their design sits very much on the shoulders of MacCormac's. Lucy Homer, project architect, says the scheme is essentially MJP's original. But was the loss of MacCormac's News Room, the project's defining space, a way of cutting corners? "No," she says. "I worked on both schemes. The MJP News Room was special. But it would have been a much darker space. It would have needed a lot of artificial lighting. What we've tried to do is concentrate on what works best in terms of construction and in ways staff and visitors will use the buildings."

The look of the News Room, all shining steel and glass with accents of bold colour, spreads out to the floors above and beyond. The overall feeling is of a sleek corporate HQ, but one with a huge technical plant set within, where things – in this case programmes – are made. Bureaucracy and broadcasting: it's a very BBC combination.

Because the public pays for the BBC, the new Broadcasting House has been made accessible, in no uncertain manner. Not only will the public be able to gaze into the News Room, they will also be able to attend concerts, and see an ambitious collection of artworks incorporated into the buildings. In fact, the courtyard is itself an enormous work of art. Called World, and created by Mark Pimlott, an artist loved by architects, the £1.6m piece has a surface that curves gently, like that of the Earth. This is crisscrossed with mosaic lines of longitude and latitude, and engraved with place names from around the world, echoing the BBC's motto: "Nation shall speak peace unto nation."

This is just the start. On top of the new wing facing All Soul's Church is Breathing, by Jaume Plensa, a Spanish artist. Costing £900,000, this inverted glass-and-steel cone beams light into the night sky and represents, says the BBC, the spirit of broadcasting, while also serving as a memorial to journalists killed while on assignment.

Although there has been criticism of this arts programme, commissioned for the BBC by the public arts agency Modus Operandi, the corporation believes it has a duty to promote and encourage art, which is why it maintains orchestras as well as buildings such as the original Broadcasting House, adorned with sculpture by Eric Gill. In this, the BBC is very different from rival broadcasters such as BSkyB.

Is it worth £1bn? Well, the whole project could certainly have been conceived with greater style, tact and efficiency. Although not the truly inspirational building the BBC dreamed of, the new Broadcasting House will probably come to be seen as an imposing yet functional HQ. You could argue that the uncertainty of its architecture perfectly reflects the uncertainty of the BBC, as it battles to stay ahead in the digital age.

• This article was amended on 27 January 2011. The original referred to vibrations caused to the building by the Jubilee Line. This has been corrected.