The agreement to set up the phone link came last month when Mr Moon's top security adviser travelled to Pyongyang for an unprecedented meeting with Mr Kim, who had then agreed to hold the inter-Korean summit.
This will be the third inter-Korean summit between both countries, after summits previously held in 2000 and 2007.
The two states remain technically at war since the 1950-53 Korean War ended in an armistice, with neither side able to claim an outright victory.
Mr Kim is also expected to hold a summit with US President Donald Trump by June. If it takes place, it will be the first meeting between a sitting US president and a North Korean leader.