Built on the edge of what was then the fastest growing city in the world, beside the railroad that made Chicago the hub of US trade, on a heap of dirt piled from the remains of the city after the fire of 1871, the Art Institute of Chicago embodies the city’s history.

Yet its stolid Beaux Arts facade is everything that the city’s most famous architecture is not. This is the city that invented the skyscraper, the city of industry, of the prairie, of the intricately clad, iron-framed behemoths that make its cityscape so recognisable. Now, a a light, steely, refined $294m extension has embedded the building back in its cultural context – and it has taken an Italian to do it.

Fading away: the museums’s Griffin Court

Its architect, Renzo Piano, has become the pre-eminent museum designer of our time. From the urban shock of Paris’s Centre Pompidou to the delicacy of the Swiss Beyeler Foundation and the Texan Menil Collection, he has built a reputation, among curators and nervy boards of trustees about to commit to many years of fundraising, as an architect of impeccable taste. His strength in the post-Bilbao era of icons is his willingness to defer to the art. He manages to deliver a blend of cool urbanity and faultless functionality.

In Chicago he has lived up to that reputation. The new Modern Wing, probably the last of this generation of US blockbuster museum extensions, holds the Art Institute’s astonishing modern collection and, with more than 250,000 sq ft of space (making a total of about 1m sq ft), makes it the largest museum in the US after New York’s Metropolitan. The building, defined by a portico, an attenuated homage to the old grand museums, faces Millennium Park, the populist sculpture garden that has been the city’s most remarkable recent success and, in particular, Frank Gehry’s exploding metal Jay Pritzker Pavilion, the world’s flashiest bandstand.

If the Gehry explodes, the Piano tinkles. Its delicate structure and sheer transparency open it out to the landscape and to the public. But it is a strange site. The railroad tracks run between the old and new wings, the mournful bells of the trains permeate the building and a new bridge housing the South Asian collections runs above the tracks. As an introduction to the new wing, the bridge is inauspicious. Clunky from the outside and the inside, the best thing about it is the views out.

The wing, though, is different. Centred on an airy top-lit atrium with galleries open to either side, it is something like a classical basilica section with nave and apses, but light and filigree in its structure. What Piano refers to as a “magic carpet”, a louvered roof, hovers above the whole structure, filtering out direct sun and binding the volumes together.

After the lightness of that central street, the galleries on the two lower floors fade a little. Well proportioned and well mannered, they fade entirely into the background; the architecture disappears. But the naturally top-lit top-floor galleries, housing the major early modernist works, are superb. Floor-to-ceiling glazing keeps the city continually in the frame, and, while it incessantly frames the skyline, the architecture of the building remains uncharacteristically inconspicuous. Neither in material nor form, space nor contrast does it grab you or surprise you. The one element that exhibits any quirkiness is the long arcing bridge that sweeps up from Millennium Park to a free public sculpture terrace, giving long views on to the sparkling waters of Lake Michigan and back to the city skyline.

External view of the building

“Chicago,” Piano tells me, “invented lightness, it invented transparency.” The city’s buildings, he continues, “are an expression of strength and light but also... fragility... and that is the story here”.

The iron-framed buildings developed as a response to Chicago’s fire led to contemporary architecture. Their strength enabled a minimal skeleton to replace masonry structures – windows could expand from floor to ceiling, floorplates could become deeper. This is the architecture of today’s city. But it was a German, Mies van der Rohe, former head of the Bauhaus, who refined the language to its ultimate conclusion. His Chicago buildings are the high point of purist modernism. But he also expressed a darkness, whether through bronze or heavy marble; his was never an architecture subservient to art.

Piano has dispensed with darkness. Now all is light. This is an exemplary museum that shows off the collection as well as it could, so it seems churlish to criticise – but it lacks a little depth. Polite, discreet, classical, Piano has refined the architecture of Chicago into a beautiful ghost of itself but it has become immaterial, spectral. Perhaps we have become so in thrall to art, to its expense and glamour, that, just as happened at New York’s Museum of Modern Art, the architecture can only fade away.