Black is a son of Eli M. Black (1921–1975), a prominent Jewish businessman who emigrated from Poland and was best known for owning the United Brands Company. His mother, Shirley Lubell, was an Artist. In 1975, his Father committed suicide by jumping out of the 44th floor of the Pan Am Building in New York City. It was later made public that, at the time, federal regulators were investigating allegations that United Brands was bribing Honduran government officials. Black received a BA in Philosophy and History from Dartmouth College in 1973 and a MBA from Harvard University in 1975. He served on the Board of Trustees of Dartmouth College from 2002 to 2011. In 2012 Black gave US$48 million toward a new visual arts center at Dartmouth College.

From 1977 to 1990, Leon Black was employed by investment bank Drexel Burnham Lambert, where he served as managing Director, head of the Mergers & Acquisitions Group, and co-head of the Corporate Finance Department. In 1990, he co-founded, on the heels of the collapse of Drexel Burnham Lambert, the private equity firm Apollo Global Management. Notable founders included: John Hannan, Drexel's former co-director of international finance; Craig Cogut, a Lawyer who worked with Drexel's high-yield division in Los Angeles; Arthur Bilger, the former head of the Drexel's corporate Finance department; Antony Ressler, who worked as a senior vice President in Drexel's high yield department with responsibility for the new issue/syndicate desk; and Marc Rowan, Josh Harris and Michael Gross, who all worked under Black in the mergers and acquisitions department.

Black is married to Debra Ressler, a Broadway Producer and sister of Ares Management co-founder Antony Ressler. They have four children. Black's wife is a melanoma survivor. In 2007, the couple donated $25 million to form the new Melanoma Research Alliance. They have committed to donating another $15 million over the next three years. He has a $43 million home in Southampton, New York. In 2012 he acquired Phaidon Press, a fine art books publisher. Apollo Global Management had no role in the purchase. It was an investment Black made privately.

Two months after the May 2012 anonymous purchase of one of four versions of Edvard Munch's The Scream, The Wall Street Journal reported that Black had been the one who had paid $119.9 million for the pastel, the highest price ever paid for a work of art at auction as of that time. In September 2012, The Museum of Modern Art announced the painting would go on view for a six-month period starting in October.

In June 2013, it was revealed that Leon Black had purchased Head of a Young Apostle, an 11-inch wide work by Raphael for £29 million after a four-party bidding war.

On December 22, 2015, it was reported that Leon Black purchased at auction a complete set of the Daniel Bomberg Babylonian Talmud for $9.3 million. According to a press release from the Sotheby's auction house, the sale is "a new world auction record for any piece of Judaica."

In June 2016, a lawsuit over the Picasso sculpture Bust of a Woman between the advisory firm Pelham Europe and art gallery owner Larry Gagosian was settled. Pelham Europe, an agent for a member of Qatar’s royal family, and Gagosian, who had resold the bust to Leon Black, both claimed ownership. The case was settled by Maya Widmaier Picasso, the owner of the sculpture. The settlement included Leon Black getting the sculpture and Widmaier Picasso paying Pelham an undisclosed amount.