Prince Philip accompanied the Queen on hundred of trips, here with George W Bush and his wife Laura in Washington in 2007
Monarchs, heads of state and PMs past and present from Sweden to India and New Zealand have been paying tributes.
The duke accompanied the Queen during hundreds of overseas visits.
"He embodied a generation that we will never see again," Australian PM Scott Morrison said in a statement.
The duke had blood ties with a number of former or current European royal households, and many of their members have been sending condolences.
Tributes came in too from the Commonwealth - 54 nations, most with roots in the British Empire and home to 2.4 billion people.
Many of those paying tribute hailed the duke for his work in schemes to help young people, and for devoting himself to numerous other public service causes.
Scott Morrison said the duke had been a constant support to the Queen and had presided as patron over dozens of organisations in Australia.
Former prime minister Julia Gillard said that while the duke had been "a man of duty, he had a sense of fun".
King Carl Gustaf said the duke had been "a great friend of our family for many years, a relation which we have deeply valued".
Swedish royal family spokeswoman Margareta Thorgren told the BBC the king and the duke had sailed together in England, adding: "That was the start of a great friendship between them."
The royal family said they remembered Prince Philip with great respect, adding: "He dedicated his long life to the service of the British people and to his many duties and responsibilities. His lively personality made an indelible impression."
Former President George W Bush praised the duke's dignity, saying Prince Philip had had a "long and remarkable life" and had "devoted himself to worthy causes and to others".
King Philippe sent a private message to the Queen, and said he hoped to speak to Her Majesty in person when possible.
He said he and Queen Mathilde would "always cherish the memories of our warm encounters".
"Truly saddened by the loss of Prince Philip, who made Malta his home and returned here so often. Our people will always treasure his memory," wrote Prime Minister Robert Abela.
Philip and Elizabeth spent two idyllic years on Malta, where he was stationed in the Navy, before King George VI died in 1952.
PM Jacinda Ardern expressed her "sincere condolences to Her Majesty and to all the Royal Family".
She said "thousands of young people have completed life-changing challenges" through the duke's Hillary Award.
PM Justin Trudeau said the duke had "contributed so much to the social fabric of our country - and the world".
He added: "Prince Philip was a man of great purpose and conviction, who was motivated by a sense of duty to others. We will fondly remember him as a pillar in the life of our Queen."
Prime Minister Narendra Modi said his thoughts were "with the British people and the Royal Family", and that the duke had had "a distinguished career in the military and was at the forefront of many community service initiatives".
PM Benjamin Netanyahu said the duke was "the consummate public servant and will be much missed in Israel and across the world".
The duke's mother, Princess Alice of Battenberg, who died in 1969, is buried at the Church of Mary Magdalene in Jerusalem.
The Duke of Edinburgh with his mother Princess Alice Of Battenberg