His sister Ruth Barenbaum said that he died in Tampa, Florida, from complications from pneumonia. "We're still in a state of shock," she said. "This was a surprise to us all."
A much-decorated combat soldier in Vietnam, Schwarzkopf was known popularly as 'Stormin' Norman' for a notoriously explosive temper.
He served in his last military assignment in Tampa as commander-in-chief of US Central Command.
Schwarzkopf became Centcom's commanding officer in 1988 and, when Saddam Hussein invaded Kuwait three years later, he commanded Operation Desert Storm, the coalition of 30 countries organised by President George Bush that drove out the Iraqis.
"Norm Schwarzkopf, to me, epitomised the 'duty, service, country' creed that has defended our freedom and seen this great nation through our most trying international crises," Bush said. "More than that, he was a good and decent man and a dear friend."
While focused primarily in his later years on charitable enterprises, he campaigned for President George W Bush in 2000, but was ambivalent about the 2003 invasion of Iraq, saying he doubted victory would be as easy as the White House predicted.
In early 2003 he told the Washington Post that the outcome was an unknown: "What is post-war Iraq going to look like, with the Kurds and the Sunnis and the Shiites? That's a huge question. It really should be part of the overall campaign plan."
Initially Schwarzkopf had endorsed the invasion, saying he was convinced that former Secretary of State Colin Powell had given the UN powerful evidence of Iraqi weapons of mass destruction.
After that proved false, he said decisions to go to war should depend on what weapons inspectors found.
In late 2004, he sharply criticised then-Defence Secretary Donald Rumsfeld and the Pentagon for mistakes that included inadequate training for Army reservists sent to Iraq and for erroneous judgments about Iraq.
"In the final analysis, I think we are behind schedule. ... I don't think we counted on it turning into jihad," he told NBC.
Although reputed to be short-tempered with aides and subordinates, he was a friendly, talkative and even jovial figure.
He also was outspoken at times, including when he described Gen William Westmoreland, the US commander in Vietnam, as "a horse's ass".
Schwarzkopf followed in his father's footsteps to West Point, graduating in 1956.
In 1966 he volunteered for Vietnam and served two tours, first as an adviser to South Vietnamese paratroops and later as a US battalion commander. He earned three Silver Stars for valour plus a Bronze Star, a Purple Heart and three Distinguished Service Medals.
After Saddam invaded Kuwait in August 1990, Schwarzkopf played a key diplomatic role by helping to persuade Saudi Arabia's King Fahd to allow US and other foreign troops to deploy on Saudi territory as a staging area for the war to come.
On January 17, 1991, a five-month build-up called Desert Shield became Operation Desert Storm as allied aircraft attacked Iraqi bases and Baghdad government facilities.
The six-week aerial campaign climaxed with a massive ground offensive on February 24-28, routing the Iraqis from Kuwait in 100 hours.
Schwarzkopf said afterward he agreed with Bush's decision to stop the war rather than drive to Baghdad to capture Saddam. But in a desert tent meeting with vanquished Iraqi generals, he allowed a key concession on Iraq's use of helicopters, which later backfired by enabling Saddam to crack down more easily on rebellious Shiites and Kurds.
After retiring in 1992, Schwarzkopf wrote a best-selling autobiography, It Doesn't Take A Hero.
Of his Gulf war role, he said: "I like to say I'm not a hero. I was lucky enough to lead a very successful war."