North Korean leader Kim arrived in Singapore on board an Air China Boeing 747 on Sunday, while US President Donald Trump landed in the city-state later in the evening.
Kim stays at the St Regis hotel and Trump at the Shangri-La, both in the Tanglin area in downtown Singapore.
More than 2,500 journalists are in Singapore to cover the event.
Singaporean Prime Minister Hsien Loong said the Kim-Trump costs Singapore about $20m to host, with half of it spent on security.
The meeting will be the first time a serving US president has sat down with the leader of North Korea.
Trump said Monday he thinks the summit will “work out very nicely".
The summit has also raised hopes of progress toward a peace treaty to formally end the Korean War after hostilities only stopped with an armistice.
The diplomacy is an extraordinary turnaround from last year, when Trump threatened the North with "fire and fury" and Kim dubbed him a "mentally deranged US dotard".
Earlier this year, Kim has met twice with both Chinese President Xi Jinping and South Korean President Moon Jae-in before heading to Singapore.
Pyongyang is demanding security guarantees and the end of what it calls a "hostile policy" toward it.
Washington is demanding the North give up its weapons in complete, verifiable and irreversible way.