"I think we have a very good chance of doing something very meaningful", Mr Trump said.
The US secretary of state also worked to ensure the release of three Americans who had been imprisoned in North Korea.
Last month the Korean leaders held their own historic meeting inside the Demilitarized Zone dividing the two sides.
Shortly after, Trump and First Lady Melania TrumpMelania TrumpTrump greets 3 American detainees freed by North Korea White House 'committed to a free press, ' says Sanders Dear Washington, you stink MORE boarded the plane to meet the Americans before accompanying them to the tarmac.
Until recently, Mr Kim and Mr Trump had been trading personal insults and threats, heightening tensions over North Korea's nuclear programme.
The announcement follows the release of three Americans who had been held in North Korea. (AAP) The trio arrived at a Washington military base during the middle of the night and were welcomed by President Trump.
Trump said again at a cabinet meeting on Wednesday that the time and place for the meeting with Kim had been decided, but would say only that it wouldn't be in the DMZ.
"We also want to thank the President for engaging directly with North Korea", the family said. After being flown to a US military base in Japan, the men were taken to Joint Base Andrews in Maryland.
State Department officials have taken great pains to keep three former North Korean detainees sequestered as they are flown back to the mainland United States.
"We have no illusions about that", he said, but added that "North Korea has taken steps that indicate this may be an opportunity for a breakthrough" on the Korean peninsula.
Kim made a decision to grant amnesty to the three Americans at the "official suggestion" of the U.S. president, said North Korea's official news agency, KCNA.
But the President saw the release of the three Americans as yet another reason for optimism as he prepares for the summit. "I said, 'Welcome home.' He said, 'God bless America, '" Hook said.
The meet marks the first time that a sitting USA president will meet with a North Korean head of state.
Meanwhile, Trump has said that "full denuclearization" is the goal of the talks. Typically, Swedish diplomats based in North Korea handle US consular affairs.
But Singapore also has rigorously sought to maintain good relationships with USA rivals, especially China, which has flexed its economic and military muscle as Beijing seeks to expand influence in Southeast Asia.
A series of U.S. administrations have sent envoys, both official and unofficial, to Pyongyang in the hope of stopping North Korea's provocative nuclear weapons program.
Their release cleared a major obstacle for the upcoming meeting, which will be the first between sitting leaders of the two countries.
Otto Warmbier, a 22-year-old American student who was detained in North Korea for 17 months, died in June 2017 after he was released by Kim's regime.
"We are happy for the hostages and their families", the Warmbiers said in a statement on Wednesday.