Dr Kissinger, who was born in southern Germany in 1923 before his Jewish family fled the Nazi regime to the US in 1938, died at his home in Connecticut, according to his consulting firm.
It said he would be interred at a private family service, with a public memorial service in New York City to follow later.
Rishi Sunak joined in tributes from serving and former US leaders and from others around the world.
“Mr Kissinger had perhaps the most profound influence on American foreign policy of any person in the last 50 years. He leaves behind a lasting legacy and his experience and insight will be greatly missed,” the Prime Minister’s spokesman told reporters.
Foreign Secretary Lord Cameron tweeted a picture of him meeting the elder statesman in recent months, when he said they discussed the war in Ukraine, Iran, Russia and China.
“Even at 100, his wisdom and thoughtfulness shone through. He was a great statesman and a deeply respected diplomat who will be greatly missed on the world stage,” the former PM said.
Chinese President Xi Jinping sent a message of condolence to Joe Biden after the passing of a man who engineered the opening up of Sino-US diplomatic relations, paving the way for China’s rise to become a global power.
Israeli President Isaac Herzog, whose country is again at war, said that Dr Kissinger "laid the cornerstone” of Israel’s 1979 peace agreement with Egypt, “and so many other processes around the world I admire".
Serving in the presidential administrations of Richard Nixon and Gerald Ford as national security advisor and secretary of state, the US official became a globally known figure from the late 1960s with his thick-rimmed black glasses and equally thick German accent.
His achievements included landmark US-Soviet arms control talks and the Paris Peace Accords with North Vietnam.
The peace accords earned him a joint award of the 1973 Nobel Peace Prize. But to his many critics, Dr Kissinger was rather a “war criminal” whose hard-nosed “realpolitik” vision of the world turned a blind eye to the excesses of bloodthirsty right-wing dictatorships in Chile, Argentina and Indonesia among others.
The Nobel prize was hugely controversial with the Nixon administration having carpet-bombed neutral Cambodia and Laos to put pressure on the supply lines of North Vietnam’s communist forces.
Cambodia lurched into a civil war that was won by the genocidal Khmer Rouge regime, which slaughtered up to two million people.
A huge effigy of him was erected outside the Royal Albert Hall by the Get Kissinger Group, which planned to hold a mock trial accusing him of being a war criminal when he visited London in 2002.
Human rights campaigner Peter Tatchell lost a legal bid to have the statesman arrested under the Geneva Convention. In his latter years, his travels were limited by pressure in Britain and other countries to hold him to account for his alleged wrongdoing.
"Kissinger winning the Nobel Peace Prize was the biggest joke of all time. He was a war criminal," Mr Tatchell told the Standard on Thursday.
"Kissinger oversaw the mass indiscriminate bombing of Cambodia in the 1970s, which killed an estimated 600,000 civilians. Although I did not succeed (with the legal bid) on a technical issue, fear of future arrest inhibited his subsequent overseas travel."
Ben Rhodes, who served as deputy national security advisor in Barack Obama’s White House, was also scathing.
“He wrote a shelf of books, many of which polished his own reputation...after all, history is written by men like Kissinger, not by the victims of superpower bombing campaigns, including children in Laos, who continue to be killed by the unexploded bombs that litter their country,” he wrote on X.
But Sir Tony Blair, whose own legacy remains coloured by the war in Iraq, said he was “in awe” of Dr Kissinger.
“If it is possible for diplomacy, at its highest level, to be a form of art, Henry was an artist,” the former prime minister said.
“Of course, like anyone who has confronted the most difficult problems of international politics, he was criticised at times, even denounced,” he added.
“But I believe he was always motivated not from a coarse ‘realpolitik’; but from a genuine love of the free world and the need to protect it.”