State media say Mr Kim is travelling on his private train. It will be his first talks with the Russian president.
The Kremlin says they will meet near the Pacific coast city of Vladivostok on Thursday, and will talk about the Korean peninsula’s “nuclear problem”.
Mr Kim is seeking support after talks with US President Donald Trump collapsed, analysts say.
Mr Trump and Mr Kim met in Hanoi earlier this year to discuss North Korea’s nuclear weapons programme, but the summit – their second – ended without agreement.
What do we know about the summit?
North Korean state media has yet to confirm a time or location for the meeting.
But Russian and North Korean national flags are already in place on Vladivostok’s Russky island, where the summit is expected to take place.
Russian soldiers have been seen marching in formation outside the train station in Vladivostok in preparation for Mr Kim’s arrival.
The North Korean leader reportedly crossed into Russia on Wednesday and stepped out of his private train at the border city of Khasan.
He was greeted by Russian women in traditional dress as part of a symbolic welcome ceremony.
What do both sides want?
This visit is being widely viewed as an opportunity for North Korea to show it has powerful allies following the breakdown of nuclear talks with the US earlier this year, the BBC’s Laura Bicker says.
The country has blamed US Secretary of State Mike Pompeo for the collapse of the Hanoi summit in February.
Earlier this month North Korea demanded that Mr Pompeo be removed from nuclear talks, accusing him of “talking nonsense” and asking for someone “more careful” to replace him.
The summit is also an opportunity for Pyongyang to show that its economic future does not depend solely on the US, our correspondent adds.
Mr Kim may also try to pressure Moscow to ease sanctions.
Analysts believe this summit is a chance for Russia to show that it is an important player on the Korean peninsula.
President Putin has been eager to meet with the North Korean leader for quite some time. Yet amid the two Trump-Kim summits, the Kremlin has been somewhat sidelined.
Russia, like the US and China, is uncomfortable with North Korea being a nuclear state.
Senior officials say the Kremlin is hoping to see a reduction in tensions on the peninsular.
Mr Putin’s foreign-policy aide, Yuri Ushakov, said the situation there had “stabilised somewhat” in recent months.
“Russia intends to help in any way possible to cement that positive trend,” he told reporters on Tuesday.
Russia has previously been involved in talks to end North Korea’s nuclear programme.
Former North Korean leader and Mr Kim’s father, Kim Jong-il, met then-Russian president Dmitry Medvedev in 2011.
A South Korean foreign ministry spokesman said Russia “shares our viewpoints” on denuclearisation and peace on the peninsula.
Nuclear activity seems to be continuing in North Korea, and the country said it had tested a new “tactical guided weapon” – thought to be a short-range missile – earlier in April.