The Metropolitan Museum of Art will take over the Whitney Museum of American Art’s Marcel Breuer building in 2015, when the Whitney opens its new museum in Manhattan’s meatpacking district, according to the terms of a real estate agreement that the museum boards are pursuing.

The Breuer building’s Brutalist concrete architecture may seem like an odd fit with the stately Classical aura of the Met. But the agreement would serve both institutions: allowing the Whitney to preserve the landmark Breuer building, at Madison and 75th Street, while providing the Met with much needed space to showcase its modern and contemporary art, an area where the institution’s holdings have long been considered its weakest link.

The Whitney had been talking to several nonprofit institutions about the possibility of taking over its uptown site because it realized it cannot afford to run two museums. Under the agreement the Met will occupy the Breuer building for at least eight years.

Under the Whitney, the Breuer building has been primarily a home for American art, but officials at the Met said they would use it as an outpost for modern and contemporary art from around the globe.

While the broad brushstrokes of the deal are set, many details are still to be hammered out, officials at the museums said. Under the broad terms approved Tuesday and Wednesday by the museum boards, the Met would move into the Madison Avenue building in four years, when the Whitney’s new museum is scheduled to open on Gansevoort Street.

With the Whitney’s groundbreaking less than two weeks away, it can proceed with its plans knowing that its financial obligations have been greatly eased. “This will give us a chance to catch our breath and get some perspective,” said Adam D. Weinberg, director of the Whitney. The Met-Whitney agreement is the second major real estate development in the New York museum world this week. The Museum of Modern Art agreed on Tuesday to take over the American Folk Art Museum’s new building on West 53rd Street because the folk museum has serious financial problems. MoMA, however, will be purchasing that building, unlike the Met, which will be operating, but not buying, the Breuer building.