Cheney died on Monday night from complications of pneumonia and cardiac and vascular disease, his family said.
The Republican - a former Wyoming congressman and secretary of defence - was already a major Washington player when then-Texas governor George W Bush chose him to be his running mate in the 2000 presidential race that Bush went on to win.
As vice-president from 2001 to 2009, Cheney fought vigorously for an expansion of the power of the presidency, having felt that it had been eroding since the Watergate scandal that drove his one-time boss Richard Nixon from office.
He also expanded the clout of the vice-president's office by putting together a national security team that often served as a power centre of its own within the administration.
Cheney was a strong advocate for the 2003 invasion of Iraq and was among the most outspoken of Bush administration officials warning of the danger from Iraq's alleged stockpile of weapons of mass destruction. No such weapons were found.
He clashed with several top Bush aides, including secretaries of state Colin Powell and Condoleezza Rice, and defended "enhanced" interrogation techniques of terrorism suspects that included waterboarding and sleep deprivation.
Others, including the US Senate select committee on intelligence and the UN special rapporteur on counterterrorism and human rights, called these techniques torture.
His daughter Liz Cheney also became an influential Republican lawmaker, serving in the House of Representatives but losing her seat after opposing Republican President Donald Trump and voting to impeach him after the January 6, 2021, attack on the Capitol by his supporters.
Her father agreed with her and said he would vote for Democratic candidate Kamala Harris in 2024.
Cheney was troubled much of his life by heart problems, suffering the first of a number of heart attacks at age 37.
He had a heart transplant in 2012.
