The museum says it will support the installation of the permanent collection in its future home in downtown Manhattan.
The new building will have three times more gallery space. The designer is Italian architect Renzo Piano.
The foundation said the grant recognizes the museum's "steadfast commitment to increasing access to the richness of American art."
The new museum is slated to open in 2015.
The metal-clad building will feature a series of asymmetrical rooftops for outdoor exhibitions. It will face the High Line elevated park and the Hudson River.
The Metropolitan Museum of Art has agreed to take over the Whitney's flagship Marcel Breuer-designed building on Madison Avenue.
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