Weinberger, who was a central figure in the Iran-Contra scandal during the Reagan administration, had been suffering from pneumonia and high fever for about a week.
He died at 5am (1000 GMT) on Tuesday in the intensive-care unit of Eastern Maine Medical Centre in Bangor, about 60km from his home in Mount Desert, said his son, Caspar Weinberger Jr.
Weinberger's wife of 63 years, Jane, his son and daughter, Arlin, were at his bedside when he died.
As head of the Pentagon, Weinberger was Reagan's zealous Cold War ally, presiding over an unprecedented peacetime military build-up costing more than $1 trillion.
He strongly opposed concessions to Moscow in arms control negotiations and pushed hard for increased defence spending, such as Reagan's Strategic Defence Initiative, a programme to develop a land-and-space-based missile shield commonly known as "Star Wars".
"He should be remembered as a world statesman, a great American patriot," Caspar Weinberger Jr said. "What he did with Reagan really brought down the Soviet Union. They stuck to their plan and simply outspent the Soviets despite all sorts of doubts here."
Weinberger (L) with Egypt's Hosni
Mubarak in 1987 in Cairo
Weinberger became caught up in the Iran-Contra scandal that bedevilled the Reagan administration.
He resigned as defence secretary in 1987 and afterwards was indicted on felony counts of lying to the independent counsel investigating the administration's programme for selling missiles to Iran and giving the proceeds to the right-wing Contra forces fighting Nicaragua's socialist Sandinista government.
He was pardoned by George Bush Sr in 1992, days before he was to go on trial.
In 1985 Weinberger had called the Iran missile plan "absurd" but supported Reagan a year later after the president decided to send missiles and spare parts to Tehran.
Condoleezza Rice, the secretary of state, said: "He was a wise man and a great public servant. He will be missed. His advice was sought even in recent times."
"He was a wise man and a great public servant. He will be missed. His advice was sought even in recent times."
secretary of state
Weinberger was also closely involved in the US policy of funding and arming Muslim volunteers fighting Soviet forces in Afghanistan in the 1980s.
Some blame this policy for paving the way for the Taliban and al-Qaida to emerge.
Weinberger began his Washington career as budget director under Richard Nixon. He also served as secretary of health, education and welfare under Nixon and Gerald Ford.
At the time of his death he was chairman of Forbes and before that had been publisher of the magazine.
Last year he debuted as a thriller writer. Chain of Command, which Weinberger co-wrote with Peter Schweizer, is the story of a staged presidential assassination and the desperate efforts of a Secret Service agent to thwart the vice-president who takes the reins and declares martial law.