Chelsea Clinton is buying a $10.5 million spread right across the street from Madison Square Park, sources told The Post yesterday.

The former first daughter and her husband, Marc Mezvinsky, signed a contract for the massive, 5,000-square-foot pad at The Whitman last month, the sources said.

Last week, ex-President Bill Clinton and former Secretary of State Hillary Rodham Clinton toured the apartment, graciously posing for photographs with the hard hats who were working at the building.

Chelsea, 33, and Marc, 35, “live in the neighborhood and found the building on their own while out walking,” a source said.

“It’s great for them, because it is in a hot neighborhood and it is very private. There aren’t hundreds of neighbors, and there is great security.”

The unit at 21 E. 26th St. is four bedrooms, with 6 1/2 bathrooms, and the family room has a full view of the park.

The master bathroom is made of Italian marble. The spread also boasts a home office and media room.

So far, Chelsea is endearing herself to the neighborhood.

She posed with her hubby and famous parents on a recent tour last week for construction workers while touring the building.

The five-story building has one apartment per floor, and a key-locked elevator.

The building will also include a gym, for those days when Clinton skips her Soul Cycle classes and Mezvinsky is away from the ski slopes.

Listing brokers Melanie Lazenby and Dina Lewis, of Douglas Elliman, declined to comment.