You must not step casually into the new Greek and Roman Galleries of the Met, as though they were some throw-away space, a cafeteria or a lobby. You should pause a moment before you pass the great Sardis Column and then proceed into the new galleries, savoring every step.

Not only is the space superbly managed in itself and in its interactions with the art on view; it is nothing less than the definitive realization of a goal nearly a century in the making, a dream that animated the minds of the museum’s founders going back nearly 140 years. It is also an eminent milestone in the completion of the Met’s master plan as promulgated by its former director, Thomas Hoving, in 1967.

The Greek and Roman Collection, together with the Old Master Galleries, has always formed the intellectual and spiritual core of the museum’s mission. But while the European Paintings group has long been enthroned at the very summit of the grand stairway, in the very center of the museum, the Greek and Roman collections have been far less fortunate.

The galleries that open tomorrow were originally planned in 1912, with a design by McKim, Mead, and White, but because of the intervening war, they did not open until 1926. No sooner had Francis Henry Taylor become director of the museum in 1940 than he resolved to transform the ground-level galleries into a public restaurant and the second story into offices. By 1954, the first floor had become the infamous Dorotheum, ironically nicknamed after high-society decorator Dorothy Draper, who was responsible for its design. Like all of Draper’s projects, there was a distinct vein of Hollywood schlock running through the place, though it probably looked a little better at its inception, with its neoclassical fixtures and sunken pool, than in later years. The place is mainly memorable for bussed trays made of plastic, and reheated macaroni and cheese — possibly fashioned from the same material.

The new design, by Kevin Roche, expands upon the original and is a substantial improvement. Although Mr. Roche’s firm, Kevin Roche John Dinkeloo and Associates, has been responsible for most of the museum’s expansion during the past four decades, its efforts have not always been happy: Despite an initial energy in the firm’s modernist idiom — most conspicuously in the 1967 Ford Foundation building at 42nd Street and First Avenue — there has long been a sense of depletion in its designs. Witness the grayish brown tonalities of the Met’s modern wing, which opened 20 years ago. Given that Mr. Roche won the 1982 Priztker Prize for his services to modernism, it is remarkable that two of his most accomplished creations should also be two of the most committed acts of neoclassicism in the past generation: the Met’s Petrie Court, which opened in 1998, and the new Greek and Roman Galleries.

In their new and, one imagines, final form, the Greek and Roman Galleries are flooded with light from a massive skylit barrel vault that spans the entire courtyard, the Leon Levy and Shelby White Court. Even in McKim, Mead, and White’s original designs, the place never looked this good. Although the firm’s decision to enhance the classical details with color might have had archaeological precedents, in the black-and-white photographs of its results, it does not appear to have been very successful. Curiously, Mr. Roche’s design is more classical, notwithstanding the original designers’ reputation as the arch-classicists of American architecture. To begin with, ugly reddish jackets have been removed from the lower shafts of the Doric columns, manifesting the glory of their flutings from the apophyge all the way to the echinus. (How pleasant, by the way, to be able to invoke the language of classical architecture for a change.) Meanwhile, the blackand-white mosaics of the original have been wisely retained and sensitively restored, uncovering a loveliness that was entirely unsuspected when the place was a cafeteria cloaked in eternal twilight.

In the very center of the space is a discreet and beautifully crafted fountain fashioned from black marble, and beyond it Central Park itself, which had been concealed by the cafeteria’s kitchen for more than two generations. Above the cornice of the ground floors, with its tasteful sequence of triglyphs, Mr. Roche has added a second story whose ionic columns and blind window surrounds have been surmounted by an oeil-deboeuf just beneath the barrel vault. It is a measure of Mr. Roche’s success that the space does not feel at all like an archaeological re-enactment, as does the Getty Villa or McKim, Meade, and White’s original designs for the Met. Rather, its classicism lives and breathes like the most natural thing in the world.

Perhaps the highest praise one can pay to the Met’s new Greek and Roman Galleries — an encomium all too rarely deserved by recent architects — is that one feels simply and emphatically happy to find oneself standing in such an inspired space.

Opens April 20 (1000 Fifth Ave. at 82nd Street, 212-535-7710).