Sheikh Sabah Al Ahmad Al Sabah died in a US hospital on Tuesday where he had been receiving treatment since July.
The Prince of Wales, 71, flew to the Gulf state on Sunday where he expressed his sympathies on behalf of the Queen.
Her Majesty wrote in a statement shared on the Royal Family's Twitter page: "Your distinguished brother devoted his life to the service of the state of Kuwait and especially its relationship with its allies and friends.
"He will be long remembered by all who work for regional stability, understanding between nations and between faiths, and for the humanitarian cause.
"I have deeply valued his friendship towards the United Kingdom, and his memorable state visit in November 2012.
"I offer your highness my sincere condolences. I offer also my sympathy to the people of Kuwait. May the long history of close companionship between our two families continue."
Sheikh Sabah's younger half-brother, Crown Prince Nawaf, 83, was sworn in as the new emir on Wednesday after deputising since the sheikh was admitted to the Mayo Clinic in Minneapolis over the summer.
The leader's funeral would have typically drawn tens of thousands of Kuwaitis onto the streets, with visits from foreign leaders and dignitaries from around the world.
But the coronavirus pandemic means the family will bury him at a private funeral.
Prince Charles has visited Kuwait seven times, including once with Princess Diana in 1989. He last visited in 2015 during a tour of the Middle East.
Sheikh Sabah was foreign minister for 38 years, establishing Kuwait as a force for peace and stability in the region.
He was also a strong advocate for its close friendship with the UK and between the royal family and the Kuwaiti ruling family.