The meeting will take place in Singapore on 12 June.
Mr Trump made the announcement, just a week after he cancelled the summit.
The confirmation came following an hour-long meeting with a top North Korean official, who delivered a letter from the North Korean leader.
“We’re going to deal,” Mr Trump told reporters moments after the meeting ended. He also said it was likely that more than one meeting would be necessary.
Mr Trump said: “I think you’re going to have a very positive result in the end. We will see what we will see.”
Mr Trump told reporters he hadn’t read the letter yet and added with a smile: “I may be in for a big surprise, folks.”
Plans for the high-stakes sit-down have been have been cast in doubt ever since Mr Trump withdrew from the meeting last week, only to announce a day later that it could still get back on track.
White House officials cast the roller-coaster public statements as reflective of the hard-nosed negotiation by the two nations.
Three teams of officials in the US, Singapore and the Korean demilitarised zone have been meeting this week on preparations for the summit.
Mr Trump’s announcement comes after top North Korean official Kim Yong Chol visited the White House today to deliver the letter.
The US president had withdrawn from the summit on 24 May with a strongly worded letter of his own, citing “tremendous anger and open hostility” by Pyongyang, but also urged Mr Kim to call him. By the next day, he was signalling the event could be back on after a conciliatory response from North Korea.
Kim Yong Chol was greeted at the White House by chief of staff John Kelly and then whisked into the Oval Office. He is the most senior North Korean to visit the White House in 18 years, a highly symbolic sign of easing tensions after fears of war escalated amid North Korean nuclear and missile tests last year.
Questions remain about what a deal on the North’s nuclear weapons would look like, though Mr Trump said he believed Mr Kim would agree to denuclearisation. Despite Mr Kim’s apparent eagerness for a summit with Mr Trump, there are lingering doubts about whether he would fully relinquish his nuclear weapons, which he may see as his only guarantee of survival.
US defence and intelligence officials have repeatedly assessed the North to be on the threshold of having the capability to strike anywhere in the continental US with a nuclear-tipped missile - a capacity Mr Trump and other US officials have said they would not tolerate.
Mik Pompeo, the former CIA chief who has traveled to North Korea and met with Kim Jong Un twice in the past two months, said he believed the country’s leaders were “contemplating a path forward where they can make a strategic shift, one that their country has not been prepared to make before”.
Yet he also said at a news conference that difficult work remains, including hurdles that may appear to be insurmountable as negotiations progress on the US demand for North Korea’s complete, verifiable and irreversible denuclearization.
“We will push forward to test the proposition that we can achieve that outcome,” he said.
Despite the upbeat messaging in the United States, Mr Kim, in a meeting with Russia’s foreign minister on Thursday, complained about the US trying to spread its influence in the region, a comment that may complicate the summit.
“As we move to adjust to the political situation in the face of US hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward,” Mr Kim told Sergey Lavrov.
North Korea’s flurry of diplomatic activity following an increase in nuclear weapons and missile tests last year suggests Mr Kim is eager for sanctions relief to build his economy and for the international legitimacy a summit with Mr Trump would provide.
But there are lingering doubts on whether he will ever fully relinquish his nuclear arsenal, which he may see as his only guarantee of survival in a region surrounded by enemies.
Mr Trump views a summit as a legacy-defining opportunity to make a nuclear deal, but he has left the world guessing since cancelling the meeting last week in an open letter to Mr Kim that complained of the North’s “tremendous anger and open hostility.” North Korea’s conciliatory response to that letter appears to have put the summit back on track.
Kim Yong Chol is the most senior North Korean visitor to the United States since Vice Marshal Jo Myong Rok visited Washington in 2000 to meet President Bill Clinton and Secretary of State Madeleine Albright.
That was the last time the two sides, which are technically at war, attempted to arrange a leadership summit.
It was an effort that ultimately failed as Clinton’s time in office ran out, and relations turned sour again after George W. Bush took office in early 2001 with a tough policy on the North.
Kim Yong Chol, vice chairman of the North Korean ruling party’s central committee, was allowed into the United States despite being on a U.S. sanctions list. And North Korean officials are not normally allowed to travel outside the New York area.