Dubbed 'Stormin' Norman', General Schwarzkopf was in charge of the coalition forces sent in to expel Saddam Hussein's troops from Kuwait in 1991.
He died in Tampa, Florida, where he retired after his last military posting as commander-in-chief of US Central Command, an official told the AFP news agency.
Former US president George HW Bush, himself in intensive care, was the first to issue a statement mourning the loss of the man that lead the war that came to define both of their careers.
"Barbara and I mourn the loss of a true American patriot and one of the great military leaders of his generation," his statement said.
"A distinguished member of that Long Gray Line hailing from West Point, General 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.
"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."
US defence secretary Leon Panetta said the decorated combat leader had "left an indelible imprint on the United States military and the country".
In a Facebook post, Colin Powell, a key member of the George W Bush administration which launched the Iraq War which toppled Saddam in 2002, called General Schwarzkopf "a great patriot and a great soldier".
"Norm served his country with courage and distinction for over 35 years. The highlight of his career was the 1991 Persian Gulf War, Operation Desert Storm. "Stormin' Norman" led the coalition forces to victory, ejecting the Iraqi Army from Kuwait and restoring the rightful government," General Powell wrote.
"His leadership not only inspired his troops, but also inspired the nation. He was a good friend of mine, a close buddy. I will miss him. My wife Alma joins me in extending our deepest condolences to his wife Brenda and to her family."
General Schwarzkopf, a burly Vietnam War veteran, commanded more than 540,000 US troops and 200,000 allied forces in a six-week war that routed Saddam's army from Kuwait in 1991, capping a 34-year career that led him to the Army's four-star general rank.
The ground campaign, which saw the US and coalition forces outflank Iraqi troop concentrations in a sweeping armoured movement, lasted just 100 hours.