In a statement Wednesday, Rumsfeld's family said he “was surrounded by family in his beloved Taos, New Mexico”.
Regarded by former colleagues as equally smart and combative, patriotic and politically cunning, Rumsfeld had a long career in government under four presidents.
After retiring in 2008 he headed the Rumsfeld Foundation to promote public service and to work with charities that provide services and support for military families and wounded veterans.
Rumsfeld is the only person to serve twice as Pentagon chief. The first time, in 1975-77, he was the youngest ever. The next time, in 2001-06, he was the oldest.
He made a brief run for the 1988 Republican presidential nomination, a spectacular flop that he once described as humbling for a man used to success at the highest levels of the government.
For all Rumsfeld's achievements, it was the setbacks in Iraq in the twilight of his career that will likely etch the most vivid features of his legacy.
The US-led invasion of Iraq was launched in March 2003.
Baghdad fell quickly, but U.S. and allied forces soon became consumed with a violent insurgency.
Critics faulted Rumsfeld for dismissing the pre-invasion assessment of the US Army's top general, Eric Shinseki, that several hundred thousand allied troops would be needed to stabilise Iraq.
Rumsfeld twice offered his resignation to Bush in 2004 amid disclosures that US troops had abused detainees at Iraq's Abu Ghraib prison, an episode he later referred to as his “darkest hour” as defense secretary.
It wasn’t until November 2006, after Democrats gained control of Congress, when Bush finally decide Rumsfeld had to go. He left office in December, replaced by Robert Gates.
Rumsfeld is survived by his wife, Joyce, three children and seven grandchildren.
Additional reporting by the Associated Press news agency.