Following the Singapore summit, Trump claimed he had accomplished what no other USA president had been able to do: get North Korea to agree to denuclearize.
Few details of summit arrangements have been released.
It triggered a months-long stalemate in negotiations as Washington and Pyongyang struggled with a process for North Korea's nuclear disarmament and the removal of US-led sanctions against the North.
But progress has been scant since then. Trump said on Twitter on Sunday.
On returning to the U.S. from the summit, Trump said in a tweet on 13 June: "There is no longer a nuclear threat from North Korea". He also said Kim knows that "without nuclear weapons, his country could fast become one of the great economic powers anywhere in the World".
It was the first time that North Korean state media have reported on Kim's second summit with Trump.
Official North Korean news agency KCNA confirmed Kim's departure from Pyongyang earlier on Saturday. His late father, Kim Jong Il, travelled all the way to Moscow by train in 2001.
The report said that the train will travel around 4,500 kilometers to Hanoi, which will take over 48 hours.
It has also been alleged that the Kim could still fly to Vietnam, and the heavily-armored train may actually be heading to the Southeast Asian nation empty, in anticipation of his return journey.
The meeting will follow their first summit in Singapore, which took place in June 2018.
His train was expected to stop at the Vietnamese border station of Dong Dang, where he will disembark and drive 170 km (105 miles) to Hanoi by vehicle, the sources told Reuters.
Security was tight before the train's arrival in Dandong, with police cordoning off the riverfront some 100 meters from the bridge with tape and metal barriers, and leading an Agence France-Presse journalist out of the area. Kim traveled to Singapore on a plane lent to him by China.
While China and South Korea are not directly involved in the summit, both have something at stake and are watching it closely.
Other senior officials, such as his de facto chief of staff, Kim Chang Son, and Kim Hyok Chol, negotiations counterpart to US envoy Stephen Biegun, were already in Hanoi to prepare for the summit.
"(President Trump) has mentioned that they'll meet again; even if there is a low-level agreement, they will seek to keep things moving", said Shin Beom-chul, a senior fellow at the Asan Institute for Policy Studies.
Vietnam's foreign ministry announced Kim would make the official visit to Vietnam in the "coming days" at the invitation of president and general secretary of the country's ruling Communist Party, Nguyen Phu Trong.
The preferred location for the summit is the Government Guesthouse, a colonial-era building in central Hanoi, three sources said Wednesday.