Last May, MoMA had reconsidered the decision following protests from architects and preservationists. It asked the firm selected to design its 100,000-square-foot expansion to determine whether the building could be integrated into the design.
On Wednesday, Diller Scofidio + Renfro informed MoMA's board that the building couldn't be preserved without undermining it architectural integrity.
The board approved the firm's decision.
The expansion will replace the folk art building with two performance and exhibition spaces. It also includes an expanded lobby.
MoMA purchased the building after the folk museum defaulted on nearly $30 million in bond debt.
The Folk Art Museum has relocated near Lincoln Center.