The pair shook hands at a luxury hotel on Singapore's Sentosa island before proceeding to talks.
After the summit the leaders signed a "comprehensive" document, promising a new relationship between the nations.
They had been discussing defusing tensions and nuclear disarmament.
The document commits North Korea to work towards "the complete denuclearisation of the Korean peninsula" and promises "new relations" between Washington and Pyongyang.
The US had demanded "complete, verifiable and irreversible denuclearisation".
There was also a commitment to build "a stable and lasting peace" on the Korean peninsula.
"I think both sides will be very impressed with the result," Mr Trump said at a signing ceremony with Mr Kim.
The US president said more details would be provided at a press conference due shortly.
Mr Trump spoke of a "special bond" with the North Korean leader and said he was "absolutely" willing to invite him to the White House.
"We've decided to leave the past behind," Mr Kim said. "The world will see major changes."
Still, analysts remain divided on what the summit will ultimately achieve. Some see it as a propaganda win for Mr Kim, others a potential path to peace.