The Republican leader said: "People are going to be very impressed and people are going to be very happy and we are going to take care of a very unsafe problem for the world".
After their historic meeting, President Trump shows North Korean dictator Kim Jong Un a sneak peek inside the presidential limo. "We will be tremendously successful". "This may very well be transformative for him as a person and for the office that he occupies", the former New Jersey Superior Court judge added.
Elsewhere scores of people were glued to TV screens at the Seoul railway station, cheering and clapping in response to Trump and Kim's cordial greetings. Once again, the flashbulbs went off, and once again Trump and Kim shook hands.
South Korea said last month the issue of US troops stationed there was unrelated to any future peace treaty with North Korea and that American forces should stay even if such an agreement were signed. Instead, the meet will set the ball rolling for a long dialogue between the two nuclear powers.
When President Donald Trump sat down to make the case for peace to North Korea's leader Kim Jong Un on Tuesday, he rolled out what amounted to a movie trailer starring the two leaders. "The world will see a major change".
Meanwhile, China praised the political resolve of the American and North Korean leaders - and said it may be time to discuss lifting sanctions on Pyongyang. "I am hoping for denuclearization and a peace agreement and also for North Korea's economy to open up".
Trump, Kim confident but body language reveals nerves at first meeting
He added that Singapore had been following developments on the Korean peninsula for a very long time. Mr Trump said earlier the highly anticipated talks represent a "one-time shot" at peace .
Donald Trump says he will have a "terrific relationship" with Kim Jong Un as they appear together for the first time in Singapore.
Rodman, sporting a black t-shirt advertising a cryptocurrency he is involved with, said he was unsure whether he would get to meet with Kim - a man he has previously described as a "friend for life".
Rodman says he took Kim's message back to the US and tried to share it then-president Barack Obama, but Obama wasn't willing to listen.
The optimistic summit was a remarkable change in dynamics from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged USA dotard".
No further clarity came during the signing itself, with Trump calling it "a pretty comprehensive document" that "we're both very honored to sign".
President Trump says North Korea's Kim Jong Un has made an "unwavering commitment" to complete denuclearization after an historic meeting in Singapore.