Schwarzkopf's sister told the Associated Press he died of complications from pneumonia.
Schwarzkopf was known popularly as "Stormin' Norman" for his notoriously explosive temper.
He lived in retirement in Tampa, where he had served in his last military assignment as commander-in-chief of U.S. Central Command. That is the headquarters responsible for U.S. military and security concerns in nearly 20 countries from the eastern Mediterranean and Africa to Pakistan.
Schwarzkopf served former President George H.W. Bush and was the mastermind behind the successful Operation Desert Shield and Operation Desert Storm. together, Bush and Schwarzkopf helped drive Saddam Hussein out of Kuwait in 1991.
Throughout that era, "Stormin' Norman" became a fixture on American TV for his on-camera briefings. He was known for his blunt speaking style.
"Barbara and I mourn the loss of a true American patriot and one of the great military leaders of his generation," Bush said in a statement. "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."
Schwarzkopf was also a decorated soldier in Vietnam. He attended the U.S. Military Academy, the U.S. Army College and received a master's degree from the University of Southern California.
"The men and women of the Department of Defense join me in mourning the loss of General Norman Schwarzkopf, whose 35 years of service in uniform left an indelible imprint on the United States military and on the country," said Secretary of Defense Leon Panetta in a statement. "His bravery during two tours in Vietnam earned him three silver stars, and set him on the path lead our troops into battle in Grenada, and then to take charge of the overall allied effort in the first Gulf War as Commander of United States Central Command. ... Today, we recall that enduring legacy and remember him as one of the great military giants of the 20th century."
President Barack Obama also released a statement on Schwarzkopf's death.
"With the passing of General Norman Schwarzkopf, we've lost an American original," he said. "From his decorated service in Vietnam to the historic liberation of Kuwait and his leadership of United States Central Command, General Schwarzkopf stood tall for the country and Army he loved. Our prayers are with the Schwarzkopf family, who tonight can know that his legacy will endure in a nation that is more secure because of his patriotic service."
The Associated Press contributed to this report.