New York financier Leon Black paid Sotheby's nearly $120 million for "The Scream," Edvard Munch's 1895 pastel of a terrified man holding his head, according to several people close to the collector.

The identity of the buyer—who set a record for a work of art sold at auction—had been one of the art world's most closely guarded secrets since the dramatic, 12-minute sale in May. Now a new parlor game will begin: guessing where the iconic artwork ends up.

Mr. Black sits on the boards of New York's Metropolitan Museum of Art and the Museum of Modern Art, setting up a potential tug of war between two of the country's most powerful art institutions. Neither owns a "Scream," aside from lithograph-print versions of it.