He arrived at the Chinese border city of Dandong after 21:00 local time (13:00 GMT) on Saturday.
The much anticipated second US-North Korea summit is scheduled for Wednesday and Thursday in the Vietnamese capital.
It follows a historic first round of talks last year in Singapore. All eyes will be on what if any progress is made towards “denuclearisation”.
The departure, confirmed by North Korean state media, is the first official acknowledgement that the talks are taking place.
The state media report said Mr Kim would pay a “goodwill” visit to Vietnam as part of the trip.
He is thought to be travelling with his sister Kim Yo Jong and one of his key negotiators, former General Kim Yong Chol.
Why are they meeting again?
“We fell in love,” Mr Trump told a rally last September of Mr Kim. “He wrote me beautiful letters.”
Despite the flowery words, the months following the first summit last June were characterised by frosty and sparse contact.
This meeting is expected to build on the groundwork of that meeting and address the thorny issue of denuclearisation, where experts say little progress has been made.
Days before the Hanoi meeting, the agenda remains unclear.
What did the last summit achieve?
The first summit last June in Singapore, between two leaders who had previously only exchanged vitriol, was certainly a historic moment.
However, the agreement they signed was vague on detail and little has been done about its stated goal of “denuclearisation”.
Donald Trump promised to scale back the US-South Korea military exercises that angered the North, but in the months that have passed many have queried what he got in return.
Moves like the dismantling of a key rocket site in the North last summer are little more more than a gesture, experts say, given the North made no commitment to halt weapons development or shut down missile bases.
However, lower-level negotiation channels have recently seen activity, which could mean more goes into a Hanoi declaration.
So what can we expect this time round?
This time round both leaders will be very conscious that expectations will be high for an outcome that demonstrates tangible signs of progress – or at least a measurable roadmap for progress.
Analysts will watch closely what concessions both sides are prepared to make for this.
Washington’s original stance was that North Korea had to unilaterally give up its nuclear weapons before there could be any sanctions relief.
But just a few days ago, President Trump said he was “in no rush” to press denuclearisation.
One possibility mooted is a declaration to officially end the Korean War. Some suggest the US will ask North Korea to put forward concrete steps, such as dismantling the Yongbyon nuclear site and missile bases, in exchange for some US sanctions relief.
Why is it happening in Vietnam?
It’s an ideal location for many reasons. It has diplomatic relations with both the US and North Korea, despite once having been enemies with the US – and could be used by the US as an example of two countries working together and setting aside their past grievances.
Ideologically, both Vietnam and North Korea are communist countries – though Vietnam has rapidly developed since and become one of the fastest growing economies in Asia, all while retaining absolute power.
Its rapid development could be used by the US to show the direction North Korea could go in should it choose to open its doors.