There’s nothing subtle about a giant ultramarine rooster looming over the city. Katharina Fritsch’s “Hahn/Cock,” the nearly 15-foot-tall chicken that now rules the roost from the rooftop terrace of the National Gallery of Art’s East Building, could be mistaken for a misplaced, third-party edition of those political-animal sculptures that are still scattered all over #ThisTown: donkeys and elephants and pandas (oh my). But visitors won’t feel déjà vu when they see D.C.’s big blue chicken at the East Building on Sept. 30, when the museum re-opens following a three-year renovation. The cock is something new.

Other details in the spick-and-span East Building are so subtle that visitors may glide right past them—or in the case of the 12,250 square feet of new galleries, right through them. That rooftop terrace is one of those new features. With a panoramic view ranging from the Michael Graves–designed courthouse annex across the street, to the Newseum, and further west to the National Archives, the terrace is instantly an essential D.C. space. It may even feel familiar. The terrace is so plainly a good idea that museum fans who know the building intimately may still wonder: Was this always here?

Designed by Perry Chin, a protégé of I.M. Pei, the East Building’s original architect, the new renovation is much more than that. Call it a revelation. Spaces that were disjointed before now feel open and connected. Enlightening new liaisons between galleries tighten the building’s flow, which felt sharp and arrhythmic once, starting with the many enjambments that interrupt the building’s atrium. The isosceles triangle, the primitive form that governs the East Building, is expressed more rationally and harmoniously now. This is not an improved museum. This is a new museum—in most every respect.

The East Building was due for some TLC. The renovation is the first of a three-phased makeover for the museum, which opened in 1978. A $39 million federal appropriation covered improvements throughout the museum’s core, including upgrades to the HVAC system and other building mechanicals. Next phases will replace the building’s multifaceted glass ceiling and other elements. The renovation called for stripping the building down to pure structure, according to Susan Wertheim, architect for the National Gallery. Accordingly, the guts are all new; the mechanicals, plus a wheelchair-compliant elevator, are now stashed away behind sleek vestibule doors painted with a silver automotive paint to match the building’s original finishes. Visitors might remember the old carpeted floors, but those are long gone. Fumed oak, inspired by the National Gallery’s West Building floors, now guides the way throughout most of the space.

Privately, the National Gallery raised $30 million from its principal donors—Victoria P. and Roger W. Sant, Mitchell and Emily Rales, and David M. Rubenstein—to take advantage of the renovation by expanding the museum. The most dramatic transformation can be found on the leg along the north side of the building, in the form of two new tower galleries, which raise the museum’s bank of rampart spaces to three. The airy, top-level tower galleries showcase major tentpoles from the permanent collection: One tower space is devoted to mobiles and stabiles by fan favorite Alexander Calder, while the other tower is split between the museum’s majestic Mark Rothko paintings and its sublime “Stations of the Cross” series by Barnett Newman.

The Newman–Rothko tower room(s) best illustrate the virtues of the East Building’s new look. In this gallery, only a single partition separating the Rothkos from the Newmans divides the otherwise uninterrupted hexagonal floor-plate of Pei’s design for the towers. (Galleries at lower levels within the towers are subdivided by many walls for hanging artwork.) Inasmuch as the renovation architects have created new space, they have reclaimed space that was poorly used. With the expansion, the museum has re-embraced glass ceilings and natural light for the Newman–Rothko and Calder tower galleries. There’s too much light pouring into the Rothko side, but no matter: The effect is dramatic. By simplifying some design decisions and reversing or restoring others, Chin and Hartman-Cox Architects have unleashed the original genius of Pei’s East Building. It wasn’t always easy to see before.

Viewers may not notice anything different about these rooms, as many of these collection highlights—the Calders, the Rothkos—always enjoyed dedicated spaces before the shake-up. (The original tower, which is still reserved for special exhibits, features a show of new works by Barbara Kruger.) But make no mistake: The configuration of the East Building is changed altogether. That’s in large part thanks to the architects, whose new linkages are a joy—especially the exquisite, fresh hexagonal staircases on each end of the building along the north side. Detailed in stainless steel with glass balustrades, they rise from the concourse in columns within each of the tower structures. Geometry rules in the East Building. Its hexagons are assemblages of triangles.

Curators also put a lot of thought into the museum during the off season. Harry Cooper, the National Gallery’s curator for modern and contemporary art, has given the East Building’s permanent collection a suitably new polish. In one sense, it’s more traditional than ever: The permanent collection galleries have gained wall text and even an audio guide, things the museum didn’t bother with before. Cooper’s textbook read of modern art—a chronological presentation that starts with early Picasso and Matisse, tours the giants of postwar modernism, and peters out in the contemporary period—is buffeted by complementary loans from the West Building. Obsessives may find on view 43 pieces from the former Corcoran Gallery of Art, whose collection the National Gallery absorbed in 2014. Folks who don’t know anything about modern art will recognize one masterpiece after another.

Perhaps more important than the collection’s newly centered narrative is its newfound flow. The highlights are so extraordinary that viewers may never pick up on the care with which these galleries are now arranged. But it’s there. The old East Building never gave a hint as to how viewers should take it on, and so the National Gallery never gave its modern art collection the treatment that it deserves. In the past, the atrium served as the hub for a set of disjointed spokes. Under the new dispensation, the permanent collection is a steady anchor. It will serve as a point of departure for special exhibitions, which for the opening include “Markers and Signs” and “Flow: Modern Art,” two trenchant thematic reads of the museum’s contemporary-art holdings by curator Molly Donovan, as well as a sampling of pledged photographs.

Also on view is “Los Angeles to New York: Dwan Gallery, 1959–1971,” a set of contemporary artworks promised to the museum by L.A. art dealer Virginia Dwan. This gift has to arrive like a hammer-blow to the Hirshhorn Museum and Sculpture Garden, which has never faced a rival for edgy contemporary artworks. No longer.

A renovation can’t fix everything that’s tilted about the National Gallery. There are still too few works by African Americans, although “Makers and Signs,” which is anchored by Glenn Ligon’s groundbreaking “Untitled (I Am a Man)” (1988), is a start. A permanent-collection gallery that assembles extraordinary pieces by Agnes Martin, Eva Hesse, and Anne Truitt, feels just a little bit like a token nod to women (although women are certainly represented throughout). A big presentation of “Lick and Lather” (1993), a series of self-portrait busts in soap and chocolate by Janine Antoni, comes too soon after the Hirshhorn gave this artist major air-time. Contributions by Latino-American and Asian-American artists are mostly missing—as are, for that matter, works by Latino, African, and Asian artists writ large. Still, with some 500 works on view, this is easily the most expansive and inclusive articulation of the National Gallery’s take on modern art to date, bar none.

No one at the National Gallery expects visitors to pick up on every gleaming new hexagon or remember where Andy Warhol’s “Green Marilyn” used to hang. Even the Tennessee pink marble for the new staircases and other spaces hails from the same quarry where the marble for the museum was sourced in the 1970s. The great redeeming quality of Chin’s renovation is that the East Building is the same—only now it’s more, better, smarter. Isolating the specific flaws with the East Building, pre-renovation, is hard to do in hindsight, since before it closed it wasn’t widely known that such major changes were in the works. But the building always lacked the practical logic that its geometry promised, and that its expansion now fulfills.

If most viewers miss the finer details, that’s no knock against the architects or curators. Many fans will simply beeline for the French small-paintings gallery or Matisse’s cut-outs. (Oh yes, they’re still here.) But the new towers and the sculpture terrace are bound to become parts of the East Building that are every bit as beloved. More importantly, the permanent collection is now delineated in a way that makes sense, structurally and categorically. And the building is a feature, not a bug.

4th Street and Pennsylvania Avenue NW. Free. (202) 737-4215. nga.gov.

Due to an editing era, we mistakenly put that the National Gallery of Art’s East Building opened in 1976. It opened in 1978. Also due to an editing error, we mistakenly listed the East Building’s address at 6th Street and Constitution Avenue NW. The correct address is 4th Street and Pennsylvania Avenue NW.