The dismantling will include collapsing its test tunnels with explosives and blocking their entrances, removing observation facilities and withdrawing guards and researchers from the site. With the structures demolished and the research and security personnel evacuated the test site will be inoperative.
The North said it planned to invite journalists from the United States, South Korea, China, Russia and Britain to inspect the process.
North Korea's six known nuclear tests have taken place in Punggye-ri, a location in the north-eastern part of North Korea where a system of tunnels has been dug under Mount Mantap.
Early on May 10, Pompeo returned to the United States from a second trip to Pyongyang together with three American prisoners released from North Korea.
Kim denied claims that North Korea is closing down "an unusable test site", according to presidential office.
"If Chairman Kim chooses the right path there is a future brimming with peace and prosperity for the North Korean people", Pompeo said at a press conference alongside South Korean Foreign Minister Kang Kyung-wha.
Until recently, Mr Kim and Mr Trump had been trading personal insults and threats, heightening tensions over North Korea's nuclear programme.
The dismantling of the test site is the latest in a series of major concessions by Pyongyang ahead of the summit with Trump.
Kim is expected to demand that the USA pledge to accept the continuation of North Korea's hereditary regime in return for vowing to achieve denuclearization on the divided peninsula in a "phased" and "synchronized" manner.
Mr Trump and Mr Kim are due to meet in Singapore on 12 June. He added that the Trump administration was focused on making sure "we didn't end up where we were before" in the talks with North Korea.
North Korean leader Kim Jong Un, left, and South Korean President Moon Jae-in raise their hands after signing a joint statement at the border village of Panmunjom in the Demilitarized Zone, South Korea. Kim has already visited China twice to meet its president Xi Jinping while Trump has sent Mike Pompeo, the current U.S. secretary of state to meet him as many times as well.
"We are starting off on a new footing - I really think we have a very good chance of doing something very meaningful".