They posed for a handshake, smiling cautiously, as they began historic talks on the nuclear standoff on the Korean Peninsula.
After their meeting, Mr Trump said “a lot of progress has been made,” and they sat down to sign a document, without giving further details.
Mr Trump told reporters the document was “pretty comprehensive” and the North Korean denuclearisation process would be starting “very quickly”.
Mr Kim said the leaders “decided to leave the past behind” and “the world will see a major change”.
“I would like to express my gratitude to President Trump to make this meeting happen. Thank you,” he said.
Mr Trump is due to give a news conference at 5:30pm (AEST).
How the historic meeting unfolded
Both men looked serious as they got out of their limousines at about 11:00am (AEST) 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.
But they were soon smiling for photos and exchanging pleasantries.
“Nice to meet you Mr President,” Mr Kim said as he sat alongside Mr Trump, against a backdrop of North Korean and US flags, beaming more broadly as the US President gave him a thumbs-up.
With the cameras of the world’s press trained on them, Mr Trump and Mr Kim built an initial atmosphere of friendship.
“I feel really great. We’re going to have a great discussion and will be tremendously successful,” Mr Trump said.
“It’s my honour and we will have a terrific relationship, I have no doubt.”
Mr Kim replied: “It was not easy to get here … there were obstacles but we overcame them to be here.”
The two then headed away for what were expected to be one-on-one talks, with translators only.
They emerged about half an hour later before moving onto a meeting involving top diplomats from both sides.
Mr Trump had said on Saturday he would know within a minute of meeting Mr Kim whether he would reach a deal.
After the meetings, the two teams and other senior officials met for a working lunch, where beef short ribs, sweet and sour pork and “Daegu Jormin”, or Korean braised cod, were served for the main course, according to the menu.
As the cameras captured the moment, Mr Trump quipped: “Very nice. Getting a good picture everyone, so we all look nice and handsome and thin … perfect.”
Summit ‘better than anybody could have expected’: Trump
The leaders emerged again after lunch and strolled together down a paved walkway before stopping and posing before the waiting news media.
“We had a fantastic meeting, a lot of progress,” Mr Trump told the reporters.
“Really, very progressive. Better than anybody could have expected, top of the line.”
Before heading to the signing ceremony, Mr Trump also gave Mr Kim a rare peek inside the US presidential limousine nicknamed The Beast.
The working lunch was the final official event scheduled for the leaders before they go their separate ways.
Mr Trump is scheduled to address the press corps and then begin the journey back to Washington.
The summit is the first between a North Korean leader and a sitting US president.
As the two leaders met, Singapore navy vessels, and air force Apache helicopters patrolled, while fighter jets and an Gulfstream 550 Airborne Early Warning aircraft circled.
Financial markets were largely steady in Asia and did not show any noticeable reaction to the start of the summit.
In the hours before the summit began, Mr Trump expressed optimism about the prospects for the meeting, while US Secretary of State Mike Pompeo injected a note of caution on whether Mr Kim would prove to be sincere about his willingness to denuclearise.
Officials of the two sides held last-minute talks to lay the groundwork for the summit of the old foes, an event almost unthinkable just months ago, when they were exchanging insults and threats that raised fears of war.
Staff-level meetings between the United States and North Korea were going “well and quickly”, Mr Trump said in a message on Twitter on Tuesday.
But he added: “In the end, that doesn’t matter. We will all know soon whether or not a real deal, unlike those of the past, can happen!”
On Tuesday morning, Mr Pompeo fed the mounting anticipation of a diplomatic breakthrough, saying: “We’re ready for today.”
He earlier said the event should set the framework for “the hard work that will follow”, insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation.