The 71-year-old, who was a Republican representative for South Carolina, died on Saturday "from a brief and sudden illness", his office said.
The statement continued: "Senator Graham's family appreciates prayers at this time and asks for privacy during this incredibly difficult period."
Emergency services responded to a call for "cardiac arrest" at Mr Graham's Washington DC home on Saturday night, according to police scanner audio obtained by our US partner, NBC News.
The senator had recently returned from a trip to Ukraine, where he met with Volodymyr Zelenskyy in Kyiv on Friday.He was scheduled to appear on NBC News' Meet The Press on Sunday.Mr Graham was elected to the US Senate in 2002 and was seeking a fifth six-year term in November.
He was a key Republican voice on defence and international affairs, with his website saying he "consistently pushed for outcomes in the War on Terror that protect our long-term national security interests".
South Carolina Governor Henry McMaster has paid tribute in a post on X, saying his family is "devastated" by the death of the "irreplaceable" politician.
"The fiercest of fighters for South Carolina and America - and a loyal and steadfast friend," he wrote. "We grieve with [Graham's sister] Darline, his family and his devoted staff.
"May God hold him gently in the palm of his hand. We shall not see his likes again."