Both leaders are in Singapore ahead of Tuesday's historic summit. North Korean leader Kim Jong Un arrived first on Sunday morning, while shortly after 15:00 (Cyprus time) US President Donald Trump arrived.
Asked by reporters about his feelings ahead of the meeting, the US President said only "very well".
In the meantime, Kim Jong Un met with Singaporean Prime Minister Vivian Balakrishnan.
"Everyone is watching the historic summit between the Democratic People's Republic of Korea and the United States, and thanks to your sincere efforts we have completed the preparations for the historic summit," the North Korean leader told Balakrishnan.
Mr. Trump flew to Air Force One a few hours after Mr. Kim touched on his tour.
Their meeting - the first between a North Korean leader and a US president - will take place on Tuesday on Sentosa Island.
The United States hopes the summit will launch a process to denuclearize North Korea.