The agent, named by the White House as Nole Edward Remagen, was in Scotland working on presidential protection when he fell ill on Sunday.
Mr Remagen, a former US marine who had 19 years’ experience in the secret service, died in Scotland on Tuesday, surrounded by members of his family.
In a statement, President Trump said: “Our hearts are filled with sadness over the loss of a beloved and devoted special agent, husband, and father.
“Our prayers are with special agent Remagen’s loved ones, including his wife and two young children. We grieve with them and with his secret service colleagues, who have lost a friend and a brother.”
Mr Trump said the agent, a five-year veteran of the marines, was “among the elite heroes” who serve in the presidential protection division of the secret service.
He added: “Melania and I are deeply grateful for his lifetime of devotion, and today, we pause to honour his life and 24 years of service to our nation.
“The incredible men and women of the United States secret service travel wherever they are needed around the world, spend long periods of time away from their families, and make tremendous sacrifices for our safety and security.
“They make up the most elite protective agency in the world, universally admired for their extraordinary skill, devotion, and courage. We are forever in their debt.”
On Tuesday, the US secret service confirmed the death “with great sadness and regret” and described the agent as a “dedicated professional of the highest order”.
It added: “The secret service thanks the medical personnel in Scotland, in addition to the members of the White House medical unit and Police Scotland who provided exceptional care and support for a member of our family.”