From the west, along the Hudson River, it looks ungainly and a little odd, vaguely nautical, bulging where the shoreline jogs, a ship on blocks perhaps, alluding to one of New York’s bedrock industries from long ago. It’s a glittery emblem of new urban capital, shipping now having gone the way of so much else in the neighborhood. From the north, it resembles something else, a factory or maybe a hospital, with a utilitarian wall of windows and a cluster of pipes climbing the pale-blue steel facade toward a rooftop of exposed mechanicals. And from the east, its bulk suddenly hides behind the High Line, above a light-filled, glass-enclosed ground floor that gives views straight through the building to the water. By moving downtown from Madison Avenue, the Whitney Museum of American Art does more than drop a cultural anchor at the High Line’s base, in the deracinated meatpacking district.

Your browser does not support this video. The move confirms a definitive shift in the city’s social geography, which has been decades coming. It ratifies Chelsea and the once-funky far West Village as something closer to what the Upper East Side used to be, say, circa 1966, the year Marcel Breuer’s Whitney building opened at 75th Street. Those neighborhoods serve up the same cocktail of money, real estate, fashion and art — except that the financiers, Hollywood stars and other haute bourgeois bohemians stand in for the old Social Register crowd. The museum’s arrival signals another shift, too. When Breuer’s Whitney opened, New York City was a much dicier proposition. His fortress, like Frank Lloyd Wright’s Guggenheim Museum several blocks north — which contrived its own enclosed, spiral version of a vertical city — reflected ambivalence about what was outside the front door. Now New York is a safe, glamorous tourist mecca and 24-hour, family-friendly spectacle, and the new $422 million Whitney building, designed by Renzo Piano, opening May 1, lets the city pour in. Grand, columnless, rectangular galleries spill onto large, stepped terraces linked by an outdoor stairway, mimicking the neighborhood’s jumble of low- and mid-rise black-tar rooftops and aging fire escapes. The museum becomes an implicit extension of the High Line: an outdoor perch to see and be seen.

Your browser does not support this video. A huge floor-to-ceiling window on the east end of the fifth floor provides an elevation over the High Line akin to that of the High Line over the street. There’s a generosity to the architecture, a sense of art connecting with the city and vice versa. I remember liking the present Museum of Modern Art before it opened in 2004. For the life of me, I can’t now imagine what I was thinking. An aged New Yorker, visiting from Florida, not long ago happened upon the new Whitney. A “kockeputzi,” she called it. Yes, it is a mishmash. But buildings take time to reveal their true selves. Mr. Piano’s galleries borrow from the old downtown loft aesthetic, with windows on both ends. They’re nonprescriptive spaces with artfully gridded ceilings for hanging movable walls in myriad configurations. They give the museum more elbow room and may prove to be the ticket: nimble and airy.

Your browser does not support this video. Or they may end up a headache: monotonous, with too much light swarming through those huge glazed walls. I’m baffled that museums today, worried about adaptability, so rarely opt for fixed and varied spaces, rooms with character. Lemming-like, they continue to ask for the empty box, as if installing a giant steel sculpture were the only need. In fact, bigger isn’t usually better. This building also has somehow to stand up to Breuer’s design, which could hardly be improved upon. The old galleries are perfectly scaled, circumscribed but fluid, serious and endearing. Even the staircase on Madison Avenue is a masterpiece of architectural craft and character, an attraction all by itself. The new museum isn’t a masterpiece. But it is a deft, serious achievement, a signal contribution to downtown and the city’s changing cultural landscape. Unlike so much big-name architecture, it’s not some weirdly shaped trophy building into which all the practical stuff of a working museum must be fitted.

Your browser does not support this video. It clearly evolved from the inside out, a servant to pragmatism and a few zoning anomalies. An eager neighbor, it also exudes a genteel eccentricity that plays off the rationalism of Mr. Piano, and of Manhattan’s street grid. Inside, irregularly weathered pine floors recycled from old factories temper a language of concrete and steel. Those same industrial materials break up the mass of the building on the outside, by turns refracting and absorbing sunlight, nudging upward, gently, the scale of a swiftly growing neighborhood.

Your browser does not support this video. Finishes are nearly everywhere refined. As in the former Whitney, elevators deliver visitors from the lobby right into the galleries, keeping priorities straight and maintaining an intimacy, between viewer and art, that was another virtue of the Breuer layout and a longstanding hallmark of the Whitney. Even the elevators are outfitted with custom-designed works by the sculptor and painter Richard Artschwager. There’s also a satellite gallery in the lobby, twice as big as the one in the Breuer building, and now free to the public. On the third floor is something the Whitney has never had, a proper theater-performance space, with an immense picture window jutting toward the Hudson. On higher floors, a vocabulary of transparency extends the views from galleries into offices and storage rooms, then onto slices of the city. I’m reminded of the Pompidou Center in Paris, which Mr. Piano designed some four decades ago with Richard Rogers. The breakthrough there was not just the inside-out-factory aesthetic but the development of a populist hangout, with a plaza in front, as opposed to a temple for art. Mr. Piano and Mr. Rogers were branded heretics.

Your browser does not support this video. A generation or two later, the new Whitney asserts that temple and hangout aren’t mutually exclusive — — that a modern art museum neither has to dumb itself down nor make itself intimidating, but can be both sanctuary and civic center. Of course that’s what most museums today claim they are. The mall-like MoMA proves how hard the balance is to strike. Gertrude Vanderbilt Whitney founded her museum in 1930 on West Eighth Street. She was one of those amazing patrons of her era, along with pioneers like Louisine Havemeyer, Abby Aldrich Rockefeller, Mary Sullivan and Lillie Bliss, who institutionalized modern art in New York City. This is the Whitney’s fourth home. When the third, Breuer’s museum, opened half a century ago, Ada Louise Huxtable, then the architecture critic for The New York Times, called it the “most disliked building in New York,” an understatement. The brooding, stone-clad upside-down ziggurat, with its moat, bridge and Cyclopean window, offended popular taste.

Ezra Stoller/Esto Ezra Stoller/Esto The New York Times Ezra Stoller/Esto Ezra Stoller/Esto Gene Maggio/The New York Times But Mrs. Huxtable saw what it really was. It married form and function, beautifully. The exhibition floors weren’t just practical and flexible. They were also particular, refined and muscular, with their gridded concrete ceilings. Outside and in, the mix of gray granite, concrete and slate conveyed extreme finesse. The building celebrated handicraft and innovation. It was not forbidding but cocoon-like, human-scaled. If Breuer’s moat was gloomy to enter, it eked out room from a constrained site and brought daylight into the basement. Artists loved it. Time proved that it even fit well into its neighborhood. A “workable museum raised to the level of architectural art,” Mrs. Huxtable called it. Fortunately, various plans over the years to expand the Breuer building, including a post-Modern makeover by Michael Graves pushed hard by powerful interests, ran aground. Any one of them would have been a disaster; public resistance produced a far better result. The Metropolitan Museum of Art has now leased the Breuer building, which clearly deserves landmark status. Memo to Met: noli tangere. Mr. Piano’s building owes a lot to Breuer’s design, even improving on the relation between the front and back of the house, reorienting the museum toward a more American kind of openness. At the same time, its industrial-looking northern facade conjures the machine aesthetic of American Precisionists like Charles Sheeler and Charles Demuth. Their works are in the opening exhibition, under a skylight that Mr. Piano devised to give views of the Whitney’s cooling towers, a ready-made still life. Mr. Piano also recognized that people want to look at other people; they want to see stuff happening, not stare at the water. So his terraces face east, toward the city, while at street level, a river view will open up when a new park replaces the Sanitation Department buildings on the pier opposite the museum.

Your browser does not support this video. The museum’s lobby will then become part of a sequence of public spaces, interrupted by the West Side Highway, from the High Line into the Hudson. The razing of those Sanitation buildings will change the calculus of scale, the Whitney potentially looming larger in the neighborhood than it does now. We’ll have to see whether that’s a problem, as we will have to wait to see whether the museum’s new lobby, with a Danny Meyer restaurant and a bookstore, proves unworkable for big crowds. Circulation is another question mark: The stairways don’t logically link up, and elevators, as anyone who ever visited the former Whitney knows, can be frustratingly slow. Still, the building is growing on me.