Trump is heading home a day earlier than expected.
Jung A-im, a university student, said she was moved while watching the landmark meeting.
The two leaders began their historic summit meeting around 8am Singapore time with a series of handshake photo opportunities. "It's rough, it's rough in a lot of places, by the way, not just there but it's rough and we will continue that and I think ultimately we will agree to something", Trump said.
Trump and Kim shook hands and posed for photos before their almost 40-minute one-on-one conversation behind closed doors.
Both men looked serious as they got out of their limousines for the summit at the Capella hotel on Singapore's Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
The actual text of the document was visible in a picture from the signing, after Trump held it up to show their signatures.
It emphasised the summit, "the first in history, was an epochal event of great significance in overcoming decades of tensions and hostilities between the two countries and for the opening up of a new future".
The pair promised in the document to "build a lasting and stable peace regime" on the Korean Peninsula and to repatriate remains of prisoners of war and those missing in action during the Korean War.
WATCH BELOW: Trump says North Korean wants denuclearization more than U.S.
The English language Korea Times welcomed the meeting as a step towards ending tensions on the Korean peninsula, which has been divided between the communist North and democratic South for almost 70 years.
But North Korea's complete denuclearization is "the only outcome that the United States will accept", Pompeo said, and sanctions will not be lifted until that happens.
He called Kim "very smart" and a "very worthy, very hard negotiator".
The optimistic summit was a remarkable change in dynamics from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn labelled the President a "mentally deranged United States dotard". "Longer than that, you start to suffer some issues", said Spoehr, a retired three-star Army general. "That is exactly the formation that the Chinese have asked for over the course of the past year, and we said absolutely not", Bremmer said.
When pressed for a breakdown on the summit expenses, he said, "I think if you calculate the price of everything in this world, you will miss out the really important things". "China is trying to play President Trump through North Korea".
Grilled by United States reporters, Trump also paid tribute to Otto Warmbier and his parents and said the college student, who fell into a coma in detention in North Korea, "did not die in vain".
"I said to everybody, I said, 'The door is open'". The second, Key Resolve, focuses more on command-and-control preparations, with a heavy reliance on computer simulation and about 12,200 USA troops and 10,000 South Koreans involved, the Pentagon said in the spring.
The question of North Korea's dismal human rights record came up a few times at the news conference, and at first, Trump said that he and Kim discussed it "relatively briefly", but later saying that "it was discussed at length outside of the nuclear situation". Moon Jae-in, South Korea's president, said after the meeting had started: "Perhaps the minds of our people are on Singapore".
Near the end of the interview clip, he tells Cuomo - through tears - "I'm so happy!"
During the signing ceremony, the two leaders sat side by side at an expansive wooden table decorated with white flowers and were flanked on either side by American and North Korean flags, The new Straits Times reported.
The group were joined by Kim's sister Kim Yo Jong at a working lunch.