Expectations for the summit were being tempered by South Korean president Moon Jae-in, who said: "The deep-rooted hostile relationship and the North Korean nuclear issue can not be resolved in one single action in a meeting between leaders".
Mr Kim said "the entire world [was] watching" while Mr Trump said he had a good feeling about the summit.
"Chairman Kim thanked Prime Minister Lee for Singapore's hosting of the US-DPRK Summit", the document adds.
North Korea's leader Kim Jong Un visits Merlion Park in Singapore, June 11, 2018.
President Donald Trump said Monday his historic summit with North Korean leader Kim Jong Un in Singapore could "work out very nicely" as officials from both countries met to narrow differences on how to end a nuclear stand-off on the Korean peninsula.
Sky News' Asia correspondent Tom Cheshire has said Mr Kim has already made clear that he is seeking economic development from the negotiations.
Image Kim Yo Jong also enjoyed a walkabout in Singapore
Just hours before what could be the most important meeting of his life, a seemingly relaxed and confident Kim Jong Un took a night on the town in Singapore, taking selfies and being greeted by cheering onlookers.
The world now needs to wait for Trump and Kim to finally meet. Now North Korean officials will nearly certainly emphasise preventing any sudden mishaps in Kim Jong Un's first visit to a foreign country other than China or South Korea since taking power, said Kim Doo-hyun, professor of protection politics at Korea National Sport University.
More recently, Trump has suggested he will raise human rights issues with Kim.
North Korea has so far presented Kim's sudden diplomatic overtures to his neighbors and to the United States as a logical next step following what Kim has claimed is the completion of his plan to develop a credible nuclear deterrent to what Pyongyang has long claimed is a policy of hostility and "nuclear blackmail" by Washington.
Cracks have also begun to appear in the "maximum pressure" campaign of economic sanctions against North Korea, even though Trump insists the USA won't loosen the screws until Pyongyang's nuclear program is dismantled.
The most common prediction that most publications made was, ironically, the unpredictability of the outcome of the Trump-Kim summit, given how both leaders tend to be mavericks.
But North Korea now deems itself "a nuclear state", and insists the US must end its "nuclear threats and blackmail" as a precondition for denuclearization, according to a statement last month from First Vice Minister of Foreign Affairs Kim Kye Gwan. -North Korea meetings, including translators, photographers and logistical staff, asking how they can be sure the American are not actually spies.
The summit could also produce some sort of declaration - short of a formal treaty - about ending the Korean War, 65 years after the armistice. -North Korea summit in Singapore. Singapore residents lined downtown streets to watch Trump's armoured vehicle, dubbed The Beast, travel from the Shangri-La hotel.