The painting, one of the most recognizable in history and the only privately-held version of Munch's famous scene, was sold at Sotheby's in New York in a dramatic 12-minute sale -- but the buyer remained anonymous.
The Wall Street Journal said it learned from "several people close" to Black that the well-known art collector had bought the painting. The $119.9 million price tag was the highest ever for a work of art at a public auction.
Black's spokesman refused to confirm or deny the report Wednesday, telling AFP: "We are not commenting on the story in the Wall Street Journal."
Leon Black, a 60-year-old New Yorker, is the founder and senior partner of Apollo Global Management, an investment fund. He is estimated to be worth $3.4 billion, according to Forbes magazine.
The 1895 work is one of four versions Munch painted. Its nightmarish central figure and lurid, swirling colors symbolized the existential angst and despair of the modern age.
Another version of "The Scream' belongs to the National Gallery of Munch's native Norway, while the remaining two belong to the Munch Museum in Oslo.