A US Air Force plane carrying the remains of an unknown number of US soldiers arrived in Osan Air Base in South Korea on Friday morning.
A repatriation ceremony is scheduled for Wednesday at Osan.
The White House said in a statement: “Today, Kim Jong-un is fulfilling part of the commitment he made to the President to return our fallen American service members.
“We are encouraged by North Korea’s actions and the momentum for positive change.”
Trump also dedicated a tweet to the North Korean leader to personally express his gratitude.
He said: “After so many years, this will be a great moment for so many families.
“Thank you to Kim Jong Un.”
Friday’s repatriation marks the 56th anniversary of the armistice that ended the 1950-1953 Korean War, which claimed the lives of thousands of US servicemen, over 600,000 Chinese, 6000,000 Korean soldiers and over a million civilians.
It may take several months of detailed DNA analysis to determine how many American soldiers can be identified and there are thousands of Americans who still remain unaccounted for after the war.
But the handover is seen as a goodwill gesture by Kim and renews hopes for progress in nuclear talks.
At the historic summit in Singapore, the North Korean leader signed a joint agreement to complete de-nuclearisation of the Korea peninsula.
However, he did not present any details on how he plans to do so, and US defence secretary, James Mattis, claimed at the end of last month that Pyongyang has not taken any steps towards dismantling its nuclear weapons.
South Korean President Moon Jae-in has previously claimed the return of remains could encourage the nuclear talks between Pyongyang and Washington.
Speaking to CBS regarding the denuclearisation process, President Trump said on Tuesday: “I’m in no real rush.
“I mean whatever it takes, it takes.”