His family moved to Cedarhurst, N.Y., on Long Island, when he was a child. As a student at Lawrence High School, he was a soccer and basketball standout. He also fostered a growing love of rap music, taping shows by influential New York disc jockeys like DJ Red Alert.

“I realized that hip-hop culture could move the world,” he told Forbes, “because it was moving me.”

Soon after graduating from Albany State University in 1990 with a bachelor’s degree in business, he followed Mr. Cohen, who had recently taken a job at SBK Records, the label founded by the industry heavyweight Charles Koppelman, the financier Stephen Swid and Martin Bandier, another music executive, known for hits by Vanilla Ice, Wilson Phillips and Jesus Jones.

After jumping to Arista, Mr. Stone became close to Christopher Wallace, the young rapper from Brooklyn known as the Notorious B.I.G., and traveled around the country with him trying to break him into the mainstream. “We spent a lot of time in cars going to hip-hop mix shows at 2 in the morning, just me and him,” Mr. Stone said in a 2015 interview with Billboard.

Mr. Stone is survived by his mother; his wife, Lauren (Gonzales) Stone; his twin sons, Jett and Charlie; his daughter, Mika; and his sister, Michelle Stone.

Mr. Stone learned he had cancer last August but continued to work until the final weeks of his life, Mr. Cohen said. It was not his first brush with cancer; when he was 20, he survived Hodgkin’s disease. The experience, he told Forbes, “gave me a heightened sense of gratitude and belief.”

“When you’re consistently going into radiation,” he said, “there are no meetings or business decisions that are more important than surviving.”