Giddiness is rarely associated with Brutalist architecture, but it might well be the sensation by which the Whitney Museum's Marcel Breuer-designed home is remembered - thanks to Jeff Koons. The former Wallpaper* guest editor and artist's vast retrospective, which opens to the public on Friday, occupies nearly every available floor, wall, and nook of the museum (approximately 2,500 sq m) and is an exuberant farewell to the 1966 Breuer Building as the Whitney prepares to move into its new space in downtown New York, designed by Renzo Piano. 'We wanted to say goodbye with a flourish,' says Adam Weinberg, director of the Whitney.

Born in Pennsylvania, Koons, 59, has lived and worked in Manhattan since 1976, but this marks his first large-scale museum presentation in New York. The challenge for the Whitney was to mount a show that would encourage visitors to look anew at the work of a celebrity artist who has simultaneously exploded and been reduced to a global cultural shorthand of stunning auction prices and gleaming, chromium steel balloon animals. ('Jeff, what are you wearing?' implored one attendee at Tuesday's press preview. Answer: Dior Homme.)

'We're at a distance now that we can assess some of these kind of mythic objects with a different perspective,' says Whitney curator Scott Rothkopf, who has spent the last five years organising the retrospective. 'I think it will be very surprising for people to see some of Jeff's most famous icons, like the Balloon Dog or Michael Jackson and Bubbles and the Rabbit, in the context of the works from which they emerged and within these series that are extremely complex in their subject matter and in their ways of making.'

Organised chronologically, the show traces Koons' multifaceted output from 1978 to works that were completed last week. New connections within and among the delineated series - such as 'Inflatables', 'Luxury & Degradation', and 'Easyfun' - click into place as one moves from room to room. A very early assemblage of coloured sponges scattered among mirrors reveals itself as a precursor to the bright and obsessively engineered forms that came decades later. The 'Banality' sculptures take a turn for the sinister when viewed together and in the round, a recurring moustache motif evokes Dali and Duchamp.

The restrospective's masterstroke is its ascension from past to present through the three main floors, so that the scale of the work grows with the building's floor plate. The drama gradually builds to a full swing celebration on the fourth floor. There are balloons, including a giant pink one affixed to the wall in an Anish Kapoor-goes-to-the-party-store moment; cake (a painted slice that stands about three metres tall); and 'Play-Doh' (2014), a massive mound of multicoloured modelling clay that Koons has been working for more than two decades to realise, eventually turning to 27 pieces of interlocking aluminium to replicate what he describes as 'a very joyous, very pop material'.

And Koons is not done yet. 'I believe completely in the work that we have here, and I hope that other people can find meaning in it, but for myself I really feel that it's about the future,' says the artist, speaking with characteristic ebullience. 'I believe that I have another at least three decades - I hope even more - to create art, and truly to be able to exercise the freedom that we all have as individuals to do exactly what we want.'