Photographs of a document signed by Trump and Kim indicate the leaders agreed to "work toward complete denuclearization of the Korean peninsula."
In exchange, Trump agreed to "provide security guarantees" to North Korea.
The document also indicates the leaders will endeavor to establish "new US-DPRK relations."
"I think our whole relationship with North Korea and the Korean peninsula is going to be a very different situation than it has in the past," Trump said at the conclusion of the landmark summit, which culminated in formal signing ceremony.
"Today, we had a historic meeting and decided to leave the past behind," Kim said through a translator. "The world will see a major change."
What precisely was agreed upon during the nearly five-hour summit was not initially clear as the two leaders sat next to each other and autographed documents in leather binders.
Trump said it was a "pretty comprehensive document," but offered no other details on what it contained. When asked about the prospects of denuclearizing North Korea -- the administration's longstanding objective -- Trump said the process would begin "very quickly."
"We had a really fantastic meeting. A lot of progress," Trump told reporters three hours later after sitting for a series of talks and a working lunch. "Really very positive. I think better than anybody could have expected."
"Top of the line," Trump said. "Really good."
Trump's threats to politely walk out of the meeting if his expectations were unmet did not materialize. Instead he predicted he could "solve a big problem, a big dilemma" alongside his new partner.
"Working together, we'll get it taken care of," Trump said.
The remarks came amid an improbable series of events that few could have anticipated even three months ago. The unlikely images of US and North Korean counterparts engaging in friendly dialogue lent the day an air of unreality. In a detailed menu, the White House said the men were served Häagen-Dazs vanilla ice cream for dessert.
Even Kim seemed to acknowledge the surreality of the day.
"Many people in the world will think of this as a (inaudible) form of fantasy ... from a science fiction movie," his translator was overheard saying as the two leaders walked down a white-columned colonnade.
The day began with Trump patting Kim on the back and placing his hand on the North Korean's shoulder as they walked into their first meeting. Their body language was openly friendly, a striking warmth given Kim's iron grip on power and dismal record on human rights. Trump's move to meet him attracted fierce criticism for normalizing a regime routinely called out for its human rights abuses, that over years has built an image of fearsome renegade regime, throwing around threats of nuclear war.
It was not clear whether Trump raised those issues during the meetings. When asked if he confronted Kim over the death of Otto Warmbier -- the American who died days after his release from North Korean captivity -- Trump did not respond.
Speaking through an interpreter, Kim alluded to the longstanding enmity between his country and the United States.
"It has not been easy to come to this point," Kim said, according to a CNN translation of his remarks. "For us, the past has been holding us back and old practices and prejudices have been covering our eyes and ears, but we have been able to overcome everything to arrive here today."
Trump nodded in agreement.
The meeting comes only months after the two men traded nuclear taunts, ratcheting up tensions and leading to fears of war.
Whether nuclear disarmament is indeed the outcome of Tuesday's summit won't be known for years, if not decades. But the dramatic act of extending his hand to one of America's longtime adversaries will forever illustrate Trump's gut-driven, norm-shattering tenure.
After the men shook hands, they repaired inside for one-on-one talks. In that first meeting they were joined only by translators, a break from standard practice of having at least one aide present for high-stakes huddles.
Later in the day, advisers joined the talks for a larger bilateral session and a working lunch. Trump was joined by Secretary of State Mike Pompeo, chief of staff John Kelly, national security adviser John Bolton and the US Ambassador to the Philippines Sung Kim, who has lent his Korea expertise to the talks.
In the lead-up to the summit, US and North Korean officials were convening contentious final-hour negotiations in a Ritz Carlton hotel here in a bid to narrow gaps on key aspects of the meeting.
It's not clear what the US side has been able to extract from the North Koreans in terms of their willingness to get rid of their nuclear weapons or allow inspectors into the country to catalog the scale of their program.
Trump took keen interest in the pageantry of the day, insisting the pictures beamed around the world reflect a commanding leader making a decisive, world-altering move. At the same time, he'd admitted he doesn't believe he requires extensive preparation to take stock of Kim.
Instead, he told reporters last weekend he would rely on "my touch, my feel" to assess the young and mercurial leader.
On Monday, the White House announced that Trump would depart earlier than expected for Washington. But before he leaves, he'll sit for an interview with his friend, the Fox host Sean Hannity, and convene a media availability for other reporters.
A US official confirmed to CNN Trump's departure was moved up by more than 12 hours because Kim set his own departure for shortly after the summit.
Tuesday's meeting, convened at a luxury hotel on the island of Sentosa, comes just three months after Trump accepted North Korea's invitation for talks on the spot. It was an extraordinarily compressed timeline for the landmark summit, one that left aides scrambling to initiate communication with the hermit nation.
The sides first spoke through intelligence channels, with US analysts working to determine Kim's true willingness to abandon a nuclear program started by his grandfather and viewed by Pyongyang as a security blanket from outside aggressors.
Pompeo, who led the outreach as CIA director, traveled twice to North Korea for preliminary talks. His sessions with Kim amounted to the most robust contact ever between the United States and the North Korean leader, providing critical information about a man about whom little is known.
But a major advancement came in late April when South Korean President Moon Jae-in met with Kim at the Korean Demilitarized Zone, a diplomatic opening that laid the basis for the future engagement with Trump. Moon has pressed for a diplomatic path to east tensions on the peninsula, fearing a more violent alternative.
Talks proceeded at multiple levels, including logistical discussions to allay Kim's fears of being deposed while traveling further afield than he ever has before as the country's leader. The site of the historic talks was a matter of intense speculation before the US President announced on Twitter it would occur here in Singapore, the flashy Southeast Asian city-state that has eagerly accommodated the spectacle.
More than 2,500 journalists have convened here, with each leader's every movement tracked carefully. A day before the summit, Trump mostly remained inside his Shangri-la hotel, emerging only to meet with his Singaporean counterpart at the presidential palace. Later in the day, he met with senior advisers and phoned the leaders of Japan and South Korea.