"We will both try to make it a very special moment for World Peace!" the BBC cites Trump's tweet.
In March, Trump stunned the world by accepting an invitation to meet Mr Kim for an unprecedented sit-down.
The pair had previously exchanged insults and threats. The breakthrough came after landmark talks between North and South Korea.
Trump's announcement came hours after he welcomed home three US detainees released by North Korea.
Their release came during a visit to Pyongyang by Secretary of State Mike Pompeo to arrange details of the meeting between Mr Trump and Mr Kim.
No sitting US president has ever met a North Korean leader. The White House said the trio were freed as a gesture of goodwill ahead of the summit, which Mr Trump earlier said he thought would be a "big success".
"I really think we have a very good chance of doing something very meaningful," he said.
The main issue under discussion will be North Korea's nuclear weapons, which the US is demanding Pyongyang give up. The North has carried out six nuclear tests, despite international condemnation and sanctions.
There has been no word from Pyongyang on its agenda or what it might offer at the summit, although a key issue is certain to be the presence of 30,000 US military personnel in South Korea, along with the removal of sanctions.