Speaking moments after the two leaders signed the unspecified document, President Trump said that he had developed a "very special bond" with Kim Jong Un. "It’s been an honor to be with you."
When asked if he would invite Kim to the White House, Trump responded that he would: "Absolutely, I will."
Standing again in front of the US and North Korean flags, where they began the historic day, Trump and Kim shook hands one final time.
"(He's) a worthy negotiator," Trump said to the gathered reporters. "He's negotiating on behalf of his people."
Trump was asked what he had learned about the North Korean leader. "I learned he's a very talented man. I also learned he loves his country very much."
Trump said they would meet again.
President Trump says denuclearization process for North Korea is starting " very, very quickly."
Asked if North Korean leader Kim Jong Un agreed to denuclearize, Trump said, "We're starting that process very quickly, very, very quickly. Absolutely."
President Trump and North Korea's Kim Jong Un are signing a joint agreement, although the exact details are still unknown.
"We're signing a very important document, a pretty comprehensive document," Trump told the waiting reporters. He said he would discuss it "at great length" at an upcoming news conference, and indicated it would be made available publicly.
Kim said he wanted to express his gratitude to President Trump for making the meeting happen.
"We had a historic meeting and decided to leave the past behind and we are about to sign the historic document," Kim said through a translator.
A US official told CNN earlier the document would acknowledge the progress of the talks and pledge to keep momentum going.
It follows a day of historic talks at Singapore's Capella Hotel, on Sentosa Island -- the first meeting between a sitting US President and a North Korean leader.
No signing had been planned at the beginning of the day, although a large amount of time had been left free after a working lunch schedule for 11:30 a.m. local time (11:30 p.m. ET).
Trump first announced there would be "a signing" shortly after midday, during a stroll with Kim around the hotel grounds.
South Korea President Moon Jae-in watched the historic meeting between President Trump and Kim Jong Un from his cabinet room in Seoul.
When the two leaders shook hands for the first time, Moon smiled, according to pictures released by the South Korean president's office.
Moon had his own meeting with Kim Jong Un in April, which was widely viewed as a success.
President Trump and North Korean leader Kim Jong Un sat down with their top advisers during a expanded bilateral meeting at the summit in Singapore.
Here's who went to the meeting:
President Trump gave Kim Jong Un a quick peek inside the presidential limousine during their talks in Singapore on Tuesday.
Television footage showed US Secret Service agents opening the door of the heavily armored "Beast" as Trump showed Kim the interior.
President Trump and Kim Jong Un will sign an agreement to acknowledge the progress of the talks and pledge to keep momentum going, a US official told CNN.
The official said he would not get ahead of the President on hard specifics of any agreement.
Trump surprised reporters by announcing there would be "a signing" in the afternoon, during a stroll around the Capella Hotel with Kim.
No official events had been planned until Trump's meeting with the press at 4 p.m. local time (4 a.m. ET).
President Trump just told reporters that he and Kim Jong Un were off to "a signing" after their working lunch.
Trump made the remark during a brief stroll around the Capella Hotel with Kim. The President also said the talks had gone "better than anybody could have expected."
There is no information on what they could be signing or whether any agreements have been reached.
No more official events were planned until Trump meets the press at 4 p.m. local time (4 a.m. ET), according to the White House's schedule this morning.
North Korea's top newspaper, the Rodong Sinmun, splashed photos of Kim Jong Un's unprecedented visit to Singapore on Wednesday, including his walking tour of the glamorous city. CNN correspondent Will Ripley, who has traveled to North Korea nearly 20 times, called the images "extraordinary."
"It's extraordinary to me because normally North Korea waits 24 hours or longer after these events, the message is vetted and edited and North Koreans find out about it after the rest of the world," CNN correspondent Will Ripley said.