The summit was the first between a sitting US president and a North Korean leader and followed a flurry of North Korean nuclear and missile tests and angry exchanges between Trump and Kim last year that fueled fears of war, Reuters reported.
"Everybody can now feel much safer than the day I took office," Trump said on Twitter.
"There is no longer a nuclear threat from North Korea. Meeting with Kim Jong-un was an interesting and very positive experience. North Korea has great potential for the future!"
On Tuesday, Trump told a news conference after the summit that he would like to lift sanctions against the North but that this would not happen immediately.
North Korean state media lauded the summit as a resounding success, saying Trump expressed his intention to halt US-South Korea military exercises, offer security guarantees to the North and lift sanctions against it as relations improve.
Kim and Trump invited each other to their respective countries and both leaders "gladly accepted," the North's Korean Central News Agency (KCNA) said.
"Kim Jong-un and Trump had the shared recognition to the effect that it is important to abide by the principle of step-by-step and simultaneous action in achieving peace, stability and denuclearization of the Korean Peninsula," KCNA said.
Trump said the United States would stop military exercises with South Korea while North Korea negotiated on denuclearization.
"We save a fortune by not doing war games, as long as we are negotiating in good faith – which both sides are!" he said on Twitter.
US Republican Senator Lindsey Graham said Trump's reasoning for halting the exercises was "ridiculous".
The United States maintains about 28,500 soldiers in South Korea, which remains in a technical state of war with the North after the 1950-53 Korean War ended in a truce not a peace treaty.
Trump's announcement on the exercises was a surprise even to South Korea's President Moon Jae-in, who has worked in recent months to help bring about the Trump-Kim summit.
Asked about Trump's comments, South Korean presidential spokesman Kim Eui-kyeom told reporters there was a need to seek measures that would help improve engagement with North Korea but it was also necessary to confirm exactly what Trump had meant.