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The 48 m high building, officially opened last week, sits on the Bergisel hill above Innsbruck, capital of the Austrian Tyrol. Its sculptural tower dominates the skyline, giving the city a unique icon.

It is a hybrid structure, containing all the facilities demanded of an international standard winter-sports venue, as well as an observation tower complete with cafe and viewing deck, from which the public can enjoy a 360º Alpine panorama.

"The challenge here was to integrate a new, initially alien element – the cafe and sundeck – into a given [ski jump] formula," says London-based Hadid. "The result is a rather unusual silhouette on Bergisel."

Hadid has fused these two elements into a single form that, viewed from the side, looks like Anubis, the jackal-headed Egyptian god of the dead, offering an outstretched hand. Curved stainless-steel cladding wraps around the volume containing the café and athletes' facilities before flowing seamlessly into the slim, arm-like jump ramp.

"It's a complex, irrational, warped surface," says assistant architect Cedric Libert. "There are no right angles. The idea was to integrate everything into a single, warping skin." The cladding is fixed to a steel frame, which is cantilevered from the monumental concrete column that contains lifts and emergency stairs.

The column sits on a subterranean box containing more training facilities and changing rooms. Visitors and athletes are ferried to the structure from the valley below on a funicular railway, which docks under a folded concrete canopy at the base of the column.

Inside the structure, facilities for the public are housed in the top two levels of the three-storeys, and the athletes and officials have the first. The groups have separate lifts to their respective areas.

In contrast with the sculptural top-piece, the 90 m long ski jump is built to the exacting specifications of international ski bodies: every dimension and radius is defined. However, the architects have managed to refine what is normally a rather ungainly structure to an elegant profile by backing the steel-framing with a bow truss strung with steel cables, which keeps the slender ramp in tension. "The ski jump is a concise piece of functional design, an instrument for high-performance sport, shaped with mathematical precision," says Hadid.

She was given the commission for the jump after winning a design competition held in 1999. The Austrian Ski Federation needed to replace the ageing jump that occupied the site, which no longer met international standards. It decided to go for something special that reflected its – and the city's – prestige. "Ski jumping in Austria is almost like football," says Libert. "It's a national sport. They wanted something that would become a symbol of the whole city."

However, the federation ruled that the ski-jumping calendar could not be affected, so the old ramp was demolished in March 2001 and the new one – minus its sculptural top – built in time for last winter's season. The ramp was used throughout the winter; work began again this spring, and the building was completed last month.

This month, work starts on a dramatic lighting scheme that will gradually shift from red to blue during the course of the evening.

This project – which cost £3m – marks the end of an era for Hadid. The Baghdad-born architect has long been one of the world's most influential and fêted designers, but until now she has built only small-scale buildings, including a tram station in Strasbourg and a fire station at Weil-am-Rhein in Germany.

However, Hadid has now entered the architectural major league, with projects for a £14m arts centre in Cincinatti and a £20m science centre in Wolfsburg, Germany, at advanced stages of construction. Projects in development include an £80m contemporary arts centre in Rome, a £100m bridge in Abu Dhabi and a £14bn masterplan in Singapore.