North's Korean Central News Agency said Mr Kim departed on Monday afternoon with his wife Ri Sol Ju and other top officials.
President Moon attended three rounds of inter-Korean summit held on April 27 and May 26 a year ago at Panmunjeom, North Korea and on September 18 to 20 at Pyongyang, North Korea to meet with Chairman Kim Jong-un of North Korea.
The trip comes as Chinese and USA officials held a second day of trade talks and as Kim prepares for a second possible meeting with President Donald Trump.
Kim's visit to North Korea's most important economic and diplomatic ally follows reports of advanced negotiations for a second summit between Washington and Pyongyang aimed at resolving the standoff over North Korea's nuclear and missile programs.
Rumors of another visit came late Monday night as a North Korean train passed into the Chinese city of Dandong under heavy security.
Unlike that occasion, when the North's state media waited until his return to announce his journey, the official KCNA news agency said on Tuesday that he was traveling on board his "private train".
In his annual New Year address last week, Kim Jong Un said that he was "ready to sit with the US president again at any time in the future and will make efforts by all means that will produce a result that will be welcomed by the global community".
Samsung says Bixby will soon work with Google Maps, YouTube
The company apparently sold millions of Google Home devices over the holidays, with smart displays being the main standout. New Google Assistant features include natural conversation, multiple voice settings, and more smart home compatibility.
Jo Song Gil, the North's acting ambassador to Rome, went into hiding with his wife in November and is seeking asylum, according to Seoul's intelligence authorities.
Asked whether China was linking the two issues in an interview Monday with CNBC, U.S. Secretary of State Mike Pompeo said, "The Chinese have been very clear to us that these are separate issues".
Another reason why North Korea may not celebrate Kim's birthday is because of his unpopularity within the country because of sanctions.
"Xi also gains from a summit with Kim - and the timing could not be any better", said Harry Kazianis, director of defense studies at the Center for the National Interest, a United States think tank.
Last month, North Korea said it would never "unilaterally" abandon its nuclear weapons unless the us first withdrew military threats and "unjust sanctions" to avoid falling into a "defenseless state". Providing the bulk of both North Korea's diplomatic support, trade and aid.
For Kim, the emphasis on his youth serves as a veiled insult in a country where the average age of senior officials was 63 in 2012, the most recent leadership transition.
"Their behavior has demonstrated that as well and we appreciate that". Kim is also expected to meet Moon again soon, possibly in Seoul. Kim did not say whether the spy agency revealed any information about Jo's current whereabouts or whether the diplomat had plans to defect to South Korea.
But even after what was seen as a blockbuster summit between Mr Kim and Mr Trump in Singapore last June - the first-ever between the leaders of the war enemies - there has been little real progress in nuclear disarmament.