Kim has committed to stopping nuclear and missile testing in the run up to the meeting, South Korean National Security adviser Chung Eui-Yong told reporters at the White House on Thursday after meeting Trump.
Even if Mr Trump and Mr Kim have agreed to meet, the key issue remains: how to denuclearise the Korean Peninsula.
South Korean President Moon has been pushing hard for a rapprochement with Pyongyang since he came into office in 2017.
Tillerson said Trump made the decision "himself" after determining the time was right for "talks" - but not formal negotiations.
Even observers who credit Trump's hardline stance with setting the stage for talks said they are waiting to see if this time is different.
"But if the USA works closely and intensively with our South Korean allies in its approach to North Korea, a summit offers the potential for starting a serious process that could move us decisively away from the current crisis", Kimball said.
Just months ago, Trump mocked Kim by calling him "little rocket man".
Kim and Trump have engaged in an increasingly bellicose exchange of insults over the North's nuclear and missile programs, which it pursues in defiance of UN Security Council resolutions, before an easing of tension coinciding with last month's Winter Olympics in the South. "Great progress being made but sanctions will remain until an agreement is reached".
He said it was the strongest indication to date of Kim's "not just willingness but really his desire for talks". "Please send my regards to Marshall Kim Jong-un and his family".
They then flew to the U.S. with a message from Mr Kim - he wanted to meet Mr Trump and was prepared to give up his nuclear weapons.
"Agreeing to a summit without a clear process, a plan and a set of preliminary talks that set the stage for success-and then sending Trump into this environment-is a huge gamble".
The announcement in the White House garden to hold the meeting was less than 24 hours after US Secretary of State Rex Tillerson had said the US "is still far from negotiating" with Pyongyang.
Following the announcement, Secretary of State Tillerson, who is now on a tour of Africa, said the meeting will take a few weeks to prepare.
What changed was his posture in a fairly dramatic way.
The other possibility is that Kim is luring the United States into negotiations and then will make demands that he knows won't be met, said Rubio.
He did not define the precise difference between talks and negotiations, and it was unclear what the two countries - still technically at war - would have to discuss if not a deal to address concerns about the North's nuclear weapons programme.
For months, it has seemed that the United Nations sanctions have been literally starving out Pyongyang. As the regime continued to pour more money into their nuclear program, while sanctions strangled their already weak economy, reports from South Korea surfaced of starving soldiers risking it all to sneak across the Demilitarized Zone (DMZ), indicating the regime may be losing its grip over the infamous One Million Man Army. Its diplomats have also played a leading role in arranging the encounter. "In the meantime, the Trump administration should continue using the toughest sanctions to maintain maximum pressure before the summit in May".
He has been able to tell his people that he made North Korea a great power; a nuclear state that has the capacity to destroy any American city.
"I'm sorry, do we not remember how very bad that photo of [then Secretary of State Madeleine] Albright toasting Kim Jong Il was?" said U.S. Naval War College professor Tom Nichols, who added that she was heavily criticized for it.