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Bilbao is collecting architectural trophies like there's no tomorrow. Frank Gehry did the Guggenheim; Norman Foster did the metro; Michael Wilford is pencilled in for the train station and Cesar Pelli is doing a skyscraper. And now this ambitious Basque city has an international airport by Santiago Calatrava.

The £130m terminal, due to open next week, is the antithesis of the flexible, extendable and largely unmemorable airport architecture of the past decade. Instead, Calatrava has created an icon. "We wanted a beacon, an emblem for the area," says airport director Segismundo López Santacruz. "We wanted something that summed up the rebirth of Bilbao and the Basque country." Calatrava, who is renowned for bridges and stations but had never designed an airport before, took the brief literally. He designed a terminal that resembles a bird taking off and a control tower akin to a torch. The metaphors are highly pertinent given Bilbao's emergence in the past few years as an economic and cultural dynamo. Yet when Calatrava was commissioned in 1989, the city was bleeding to death, its heavy industries decimated and its image tarred by the activities of Basque separatist group ETA.

"The form of the building is about flying, it's about daring," says Andres Caride, Calatrava's project architect. "Bilbao has become a bit of a cult place, but at the time, Santiago thought, what better way to create an international gateway to a city nobody knew?" The international terminal replaces Bilbao's tiny domestic airport, rendered obsolete by the city's rapid emergence as a regional transport hub. Set at the foot of a verdant hill, across the runway from the existing terminal, the virgin site allowed Calatrava to design everything from scratch. "The nice idea about this project is that we could think of it as a whole, including the car parks and the landscaping," says Caride. "The approach by road is important – you arrive from above and drive down towards it." Viewed through the window of a landing jet, the purity of the concept is even more apparent. The angular white terminal sits alone in the landscape, aloof from the sprawl that engulfs almost every other airport. Calatrava's great stroke of luck was that the hangars, warehouses and car-hire sheds are already established in the village of Sondika across the runway. To prevent the E E obligatory 3000-space car park messing up the view, the architect has buried the four-storey structure in a turfed mound.

Despite the interminable construction period, mounting costs and numerous postponed openings, Bilbainos have taken the building to their hearts, nicknaming it "la paloma" – the dove. "It's beautiful," says taxi driver Javier Puertas. "It's just as spectacular as the Guggenheim." The roof's pointed beak has already knocked Gehry's masterpiece off the front cover of several local guidebooks.

The 32 000 m² terminal is vintage Calatrava, featuring a virtuoso superstructure of white-painted steel atop a two-storey platform of cast concrete. To enter, passengers pass beneath a curving, cantilevered canopy of raw concrete, then ascend narrow escalators wedged between heavy columns. This is the least successful part of the building, as the elephantine concrete creates spaces that are dark and alien. The entrance faces north, and a nasty green slime has already added a grotesque patina to some of the columns. "Calatrava was born in Valencia where there's a lot of sun, but there isn't much here," says Estibaliz Fernandez, explaining the premature weathering. Fernandez, a young Basque airport official detailed to show me around the building, is delightfully opinionated and full of gossip.

"They say the airport is not big enough for Bilbao, which is now a very important city because of the Guggenheim," she confides, as the escalator carries us up through the concrete bowels. "They're thinking of extending it. But Calatrava doesn't want them to do it. He doesn't want them to spoil the design." The escalator deposits us on a curving internal passage running the 150 m length of the terminal. Formed of repetitive, arching concrete ribs and totally devoid of the usual clutter of airport signage and furniture, the passage has the ethereal quality of a cloister. Glass panels between the ribs offer views down into the baggage reclaim hall, another mysterious vaulted space reminiscent of a cave. "It's a bit claustrophobic," says Fernandez. She hurries me on up another escalator that transports us up to the highlight of the building.

The departure hall is spectacular: a lofty triangular space topped by a soaring roof, ribbed to resemble the plumage of a pair of partly folded wings. Low on the airport's land-side, the roof rises towards the runway, culminating in a sharp point, reminiscent of Concorde's snout, 29 m above the ground. Check-in desks are ranged along the edges of the hall, 18 on each side. Floor-to-ceiling glazing floods the 7000 m² space with natural light and allows passengers to see awaiting planes from the moment they arrive in the hall. An underfloor cooling and heating system keeps the hall – and the rest of the building – entirely free of ducting.

The triangular hall naturally funnels passengers towards the apex, where passport control and X-ray machines are located. We pass an angular wedge of stainless steel – the desk where Fernandez will be stationed. "It's too small," she moans. Once through the security checks, passengers enter the departure zone: a 337 m long, four-storey gallery stretching parallel to the runway. Glazed from top to bottom, the structure does away with the traditional departure-lounge configuration and instead feels like a grandstand from which to view aircraft. Set at intervals along the gallery, six gracefully arching pontoons stand ready to receive the first aircraft.

Fernandez begins fault-hunting again. The toilets are too small, she says, the surfboard-shaped benches too uncomfortable. She has a point: everything within the terminal is subservient to the architect's grand concept, and humdrum elements such as toilets and shops have been squeezed into impossibly tight corners in order to preserve the clean lines.

The terminal was designed to handle 6 million passengers a year – more than double the present number – but already AENA, the Spanish airport authority, is talking about a potential 10 million a year. It is drawing up plans to lengthen the departure gallery laterally in both directions to allow more planes to dock, and intends to create a new underground baggage-handling area.

Airport director López Santacruz admits that passenger demand has forced AENA to rethink its plans for the airport. "It's making it very difficult to plan our infrastructure," he says. AENA hopes to come to some arrangement with Calatrava, he says, to ensure the expansion is faithful to the architect's vision. But if Calatrava refuses to co-operate, would AENA appoint someone else? "If he doesn't want to work on it, we would have to look for a different architect," says López Santacruz. But this is Bilbao, city of icons, and that would be sacrilege. He adds: "If you had a Michelangelo painting, you'd want Michelangelo to make any alterations."