The South Carolina lawmaker died after a "brief and sudden illness," his office posted on social media platform X.
US media said emergency personnel had responded to a call for cardiac arrest at his Capitol Hill home on Saturday night, local time.
Graham, just back from a trip to Ukraine, had been scheduled to appear on NBC's Meet the Press interview program on Sunday morning, the network said.
Shortly after his death was announced, Trump called Graham "one of the greatest people and senators I have known" and a hard-working patriot.
Ukrainian President Volodymyr Zelenskiy said he was deeply saddened, calling Graham "a true defender of freedom and the values that make our world safer".
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."
Graham told CNN in 2015 that Trump was "a race-baiting, xenophobic, religious bigot", adding, "He doesn't represent my party. He doesn't represent the values that the men and women who wear the uniform are fighting for."
Later, after becoming a loyal supporter and frequent golf partner, Graham still 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.
"Israel has lost one of its greatest friends. America has lost a great patriot. I have lost a beloved friend," Israeli Prime Minister Benjamin Netanyahu said in a statement.
Graham, a frequent visitor to Ukraine, met President Volodymyr Zelenskiy in Kyiv on Friday. They discussed Ukraine's air defence needs and a Russian sanctions bill, Zelenskiy said.
Zelenskiy noted that Graham had visited Ukraine 10 times since Russia's full-scale invasion in 2022.
In a social media post, he wrote: "We will always be especially grateful for the recognition of our people and words of admiration for the courage of Ukraine's defenders."
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.
