It was the third meeting between the two leaders in just over a year and will raise hopes for a revival of stalled nuclear talks.
Trump briefly crossed a military demarcation line that had for years represented a tense Cold War border, into the North, becoming the first ever U.S. president to set foot in the reclusive country.
Moments later Kim joined Trump to step into the South Korean side.
"It's a great day for the world," Trump said as he and Kim stood together amidst a throng of press photographers, aides and bodyguards.
Kim looked relaxed and happy as he chatted with Trump.
"This is an expression of his willingness" to work towards a new future, Kim said.
Kim said it would be a great honour if Trump visited his capital of Pyongyang.
Trump arrived in South Korea late on Saturday for talks with President Moon Jae-in after attending a Group of 20 summit in Osaka, Japan, during which he made a surprise, spur-of-the-moment offer to meet Kim, who accepted it.