The former general spent the holidays with his family and had not long suffered from pneumonia, his sister Ruth Barenbaum told The New York Times.
He leaves behind a wife and three children.
Former Secretary of State Colin Powell told NBC News he will remember Schwarzkopf as a "close buddy," a great patriot and a great soldier.
Aides to former President George H.W. Bush, who is hospitalized with a persistent fever in a Houston hospital, released a statement saying: "Barbara and I mourn the loss of a true American patriot and one of the great military leaders of his generation. A distinguished member of that Long Gray Line hailing from West Point, General Norm Schwarzkopf, to me, epitomized the 'duty, service, country' creed that has defended our freedom and seen this great Nation through our most trying international crises.
"More than that, he was a good and decent man -- and a dear friend. Barbara and I send our condolences to his wife Brenda and his wonderful family," the statement said.
Bush awarded Schwarzkopf the Presidential Medal of Freedom for his Desert Storm service, and Britain's Queen Elizabeth II made him an honorary knight.