The National Museum of African American History and Culture on Washington’s National Mall—opening in September—has been a long time coming. Architect David Adjaye’s radically inventive design will make sure it's unforgettable.

In a profession that rewards age and experience, the British-Ghanaian architect David Adjaye has hit the top without having to wait his turn. He has buildings or ongoing projects on four continents. He spends a third of his life on airplanes; maintains offices in London, New York, Berlin, and Accra; and rarely spends two consecutive nights in the same bed. He’s on the short list of architects now being considered for President Obama’s library. And on September 24, two days after his fiftieth birthday, the Adjaye-designed National Museum of African American History and Culture opens on the National Mall, in Washington, D.C. It is by far his most important building to date, and one of the most keenly anticipated monuments of our time.

The exterior of the building has been finished for several months. It’s a tiered, upside-down ziggurat—three stacked square boxes with outward-leaning walls, resting on a glass-and-steel base. The zigzag silhouette is shrouded in open-work aluminum panels painted dark bronze—in striking contrast to its white-marble and limestone neoclassical neighbors. It’s a daring contemporary design based on Yoruba tribal motifs, built on the last full site in Pierre Charles L’Enfant’s original plan for the Mall, and a stone’s throw from the White House.

Three years ago, I sat with David Adjaye under a tree, looking at what was then a five-acre hole in the ground. He showed me one of the panels on his iPad and explained that they had been adapted from ornamental iron castings made by slaves and former slaves in Charleston and New Orleans. Now the exterior of the building is in place, and for all its nonconformity, it looks completely at home. “It’s about architecture, but also about memory and history,” Adjaye says when we meet at the site on a cloudy afternoon in mid-May. “I got exactly what I wanted on the exterior, which was a dark, brooding, bronzelike building.” Before going inside, he points out what he calls the “oculus,” a circular raised platform at the west entrance through whose glass windows you can see the room below. “We found out that this spot was once a slave market, right on the Mall,” he says. “The oculus is like a slave pedestal, levitated off the ground. I’ve tried to make every decision here have some history.”