The South Carolina lawmaker died after a "brief and sudden illness," his office posted on social media platform X.
NBC News said emergency personnel had responded to a call for cardiac arrest at his Capitol Hill home on Saturday night, local time.
Shortly after his death was announced, Trump called Graham "one of the greatest people and senators I have known" and a hard-working patriot.
During the 2016 campaign, during which Graham was among many Republicans who lost the presidential nomination to Trump, he posted on social media: "If we nominate Trump, we will get destroyed ... and we will deserve it."
Later, after becoming a staunch supporter, Graham publicly disagreed with Trump's early 2025 decision to pardon about 1500 of the president's supporters who attacked the US Capitol on January 6, 2021, saying it could lead to more violence.
A defence hawk, Graham "consistently pushed for outcomes in the War on Terror that protect our long-term national security interests", his website said. He was a prominent supporter of Israel and Ukraine and opponent of Iran.
Israeli Defence Minister Israel Katz posted on X that he was deeply saddened by the death of Graham, "who stood with Israel at its most difficult moments".
On Friday, Graham said China could play a decisive role in pressuring Russia towards peace talks, helping end its war in Ukraine.
Graham, a frequent visitor to Ukraine, met President Volodymyr Zelenskiy in Kyiv. They discussed Ukraine's air defence needs and a Russian sanctions bill, Zelenskiy said.
Graham said bolstering Ukraine's military capabilities and aligning sanctions with a diplomatic push could force Moscow into talks.
"The road to ending this war, the road to peace, passes through Beijing more than it does (through) Washington, Kyiv, or Moscow," Graham told reporters at Kyiv's Mykhailivska Square.
"China has an oversized influence. I'd like them to use their influence for the good of the world."
"I don't believe (Russian President Vladimir) Putin is there yet, but it wouldn't take much to get him there."
Graham, a former US Air Force lawyer and member of the South Carolina Air National Guard, was elected to the US Senate in 2002.
Before that, he was elected to the US House of Representatives in 1994 for South Carolina's 3rd congressional district, according to his website.
He was not married and lived in Seneca, South Carolina.
