The agent was part of Trump's security detail when he visited Scotland last week.
He had been receiving "critical care" from medics in Scotland after falling ill while carrying out his duty to protect the president on Sunday, but died on Tuesday morning surrounded by family members.
The 42-year-old agent, identified as Special Agent Noel E. Remagen, was working on protection for National Security Adviser John Bolton on the midnight shift.
"We ask for your thoughts and prayers for his family, friends and colleagues".
White House Press Secretary Sarah Sanders also expressed condolences.
Agent Remagen, who Vice President Pence called "a courageous American", leaves behind his wife and two children.
Trump said, "Melania and I are deeply grateful for his lifetime of devotion".
The man's name has not yet been released to give his family some privacy at this time.
Alongside Trump's team a major operation was organised by Police Scotland with thousands of cops present during Trump's stay at the golf resort and hotel - as well as keeping protestors in check. We are so sorry for your loss and are grieving with you, ' she said.
The agent's identity and what he was doing at the time was not provided by the Secret Service.
President Donald Trump waves as he boards Air Force One at Love Field in Dallas, Friday, May 4, 2018, after speaking to the annual Nation Rifle Association convention.
Remagen's LinkedIn profile doesn't offer much insight to his life, but highlighted his many years' worth of service to the Secret Service. Christopher J. Smith was the last agent listed on the Wall of Honor: he died of a heart attack on March 25, 2005. A GoFundMe page set up to cover funeral expenses has raised more than $49,000.
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