WASHINGTON, D.C. — When the Robert and Arlene Kogod Courtyard opened last week at the Smithsonian’s American Art Museum and National Portrait Gallery, the public was introduced to a poetic social space — a formerly outdoor courtyard now topped by an undulating glass-and-steel roof that connects the two museums. Norman Foster, the architect of the new space, described this arc of glass as a “cloud floating gently on the skyline.”

With this elaborate structural innovation, the two museums have completed the final stage of the renovation and refurbishment of their joint premises in the former U.S. Patent Office. It is to their credit that the directors — Elizabeth Broun of the American Art Museum and Marc Pachter of the National Portrait Gallery — recognized the advantages of converting their 28,000-square-foot courtyard into an important space, usable no matter what the weather. Following an international competition, they chose Foster + Partners — the team that designed the glass-enclosed Great Court of the British Museum in London — to transform the courtyard into indoor space.

The newly enclosed area possesses the convivial atmosphere of an Old World town square — with modernity overhead. The original buildings’ three-story façades that face the courtyard are made of gray granite; they incorporate strong horizontals, ornate cornices, and the rhythmical verticality of Doric pilasters. At the grand entrance, the pedimented, bowed façade in buff sandstone is a graceful counterpoint to the wave in the glass canopy above it. At night, various gallery rooms are lit up at random and give the impression of lived-in spaces.

Adding to the impression of an outdoor square, landscape architect Kathryn Gustafson created a temperate design with eight asymmetrically placed, rectangular, white marble planters filled with black olive trees. They are underplanted with what she calls “a green rumble” of camellias, ferns, and pittosporum, among other plants. Two 32-foot-tall ficus trees frame the bowed entrance in a stately manner. A simple plinth, also of the same white marble used in the museum’s corridors, provides comfortable seating, “like a rock in a national park,” she said. But Ms. Gustafson’s true magic is typically her inclusion of water; here, it is a long scrim of water that flows in a four-part rectangular strip over the two-tone gray granite floor. It is only one-quarter-inch deep, but it nevertheless reflects at slow speed the entire façade and the trees. For public events, the water disappears.

Lighting designer George Sexton, who is known for his pure white lighting of museum interiors and artwork, has introduced the kind of palette that the British artist John Constable would paint into the air of his cloud studies. The so-called hills and valleys of the canopy could not be overlit to compete with other Washington illuminations, so the colored lights at night are directed downward in a succession of blues, greens, pinks, purples, magentas, reds, and yellows. They are a takeoff also from what Mr. Gustafson described as rich velvet hangings in a 19th-century ballroom. The trees stand out in this eerily beautiful light, with the planters appearing to float in rings of their own light. Tiny white lights inserted at cross points of the grid above provide an ambient glow akin to starlight.

With this glass roof structure, the architects faced a number of technical challenges. Because of Washington’s climate, the Foster team had to employ different architectural and engineering approaches than they did for the British Museum. Preservation issues also prohibited the roof from resting on the building itself. Another stipulation required that the new roof not rise above the building’s Parthenon-like entrance as seen from Pennsylvania Avenue.

But the challenges led to creative solutions. The head of design at Foster + Partners, Spencer de Grey, explained that the glass-and-steel canopy, with 864 individual diamond-shaped panels of fritted glass, is borne aloft like a magic carpet by eight columns of anodized aluminum. The dark rubber gap space in between disappears at night, giving the roof its floating appearance. Only 36% of natural daylight pours through the glass, which eliminates harsh sunlight. And in a triumph of acoustical control, strips from 9,000 pairs of recycled denim jeans were inserted along the steel grid beams to muffle noise.

The transformation of this outdoor space into indoor space seems fitting for a site that has undergone so many changes already. In Pierre-Charles l’Enfant’s 1792 plan for the nation’s capital, this plot of land — uphill from Pennsylvania Avenue — was designated for a pantheon to national heroes that would complete a triangle with the U.S. Capitol and the White House.

Instead, President Andrew Jackson authorized the construction of a patent office, a temple of progress symbolizing future ingenuity and industry — which was more fitting culturally to the new democracy. The resulting building, a handsome Greek Revival structure with a double Doric entrance colonnade, wraps around four city blocks and includes the central courtyard. In 1968, it was converted from the patent office to back-to-back museums. And now, Washington has an important new civic space — one of the largest in the city. It will surely be a gathering place for official events in the nation’s capital, not the least of which will probably be presidential inaugural balls.